Ep4 Conjugate n Division of complex numbers Linear Algebra

>> DOWNLOAD LINK 🎞️ #1 <<

>> DOWNLOAD LINK 🎞️ #2 <<

>> COPY / PASTE LINK PLEASE 🎵 MP3 <<

>> YOUR LINK HERE: ___ http://youtube.com/watch?v=p2feqqKcnuk

this episode teaches how to find the conjugate of a complex number as well as how to perform divisions.","styleRuns":[{"startIndex":0,"length":103,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":103,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CNsBELsvGAIiEwi--t33pdKLAxV1i4wIHcOlOGM=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC3AyZmVxcUtjbnVrGAYyJSIRIgtwMmZlcXFLY251azAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CNsBELsvGAIiEwi--t33pdKLAxV1i4wIHcOlOGM=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CNoBELovIhMIvvrd96XSiwMVdYuMCB3DpThj"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"jouS0z3XHN0","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/jouS0z3XHN0/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgZShlMA8= rs=AOn4CLAsJbU2lOXe00ft4crl2Q9org642g","width":168,"height":94},{"url":"https://i.ytimg.com/vi/jouS0z3XHN0/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLBhA5HFy2nWrRBvqCFrACZ0a2shHw","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Ep5 Modulus AND Argument (Linear Algebra) by Einstein’s Mechanics 4,571 views 2 years ago 30 minutes"}},"simpleText":"Ep5 Modulus AND Argument (Linear Algebra)"},"longBylineText":{"runs":[{"text":"Einstein’s Mechanics","navigationEndpoint":{"clickTrackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@Einsteins-mechanics","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCK4cR9c8C199wQajlrS2eBQ","canonicalBaseUrl":"/@Einsteins-mechanics"}}}]},"publishedTimeText":{"simpleText":"2 years ago"},"viewCountText":{"simpleText":"4,571 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"30 minutes, 23 seconds"}},"simpleText":"30:23"},"navigationEndpoint":{"clickTrackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWRI6b3ylKrV97OnAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=jouS0z3XHN0","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"jouS0z3XHN0","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=8e8b92d33dd71cdd ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=757500 mt=1740055497 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Einstein’s Mechanics","navigationEndpoint":{"clickTrackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@Einsteins-mechanics","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCK4cR9c8C199wQajlrS2eBQ","canonicalBaseUrl":"/@Einsteins-mechanics"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/U-_ezeiXRZzCFVBOWKLHwcyzCWjXur80kcV-j1jZ-MjhKkVGCHmV_thXqDSdFjFpYjZQhU2PpA=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGNA3bnc7rPa5MWOAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"4.5K views"}},"simpleText":"4.5K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CNgBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNgBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"jouS0z3XHN0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNgBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["jouS0z3XHN0"],"params":"CAQ%3D"}},"videoIds":["jouS0z3XHN0"]}},{"clickTrackingParams":"CNgBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CNkBELlqIhMIvvrd96XSiwMVdYuMCB3DpThj"}},"popupType":"TOAST"}}]}},"trackingParams":"CNgBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CNcBENGqBRgGIhMIvvrd96XSiwMVdYuMCB3DpThj","offlineVideoEndpoint":{"videoId":"jouS0z3XHN0","onAddCommand":{"clickTrackingParams":"CNcBENGqBRgGIhMIvvrd96XSiwMVdYuMCB3DpThj","getDownloadActionCommand":{"videoId":"jouS0z3XHN0","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CNcBENGqBRgGIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGM=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"Cgtqb3VTMHozWEhOMA%3D%3D","commands":[{"clickTrackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGM=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CNYBEI5iIhMIvvrd96XSiwMVdYuMCB3DpThj","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGM=","hasSeparator":true}}],"trackingParams":"CNMBEKQwGAAiEwi--t33pdKLAxV1i4wIHcOlOGM=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"30 minutes, 23 seconds"}},"simpleText":"30:23"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNUBEPnnAxgBIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"jouS0z3XHN0","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CNUBEPnnAxgBIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"jouS0z3XHN0"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNUBEPnnAxgBIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CNQBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNQBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"jouS0z3XHN0","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNQBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["jouS0z3XHN0"],"params":"CAQ%3D"}},"videoIds":["jouS0z3XHN0"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CNQBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Ep5 Modulus AND Argument (Linear Algebra) - 30 minutes - Go to channel - Einstein’s Mechanics - 4.5K views - 2 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"ceaNqdHdqtg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/ceaNqdHdqtg/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCjdduhJbIDlByaTNFeTmFV0evHhA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/ceaNqdHdqtg/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLDEaqPOZAAdpnI0avP46LJBChdRgQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"The strange cousin of the complex numbers -- the dual numbers. by Michael Penn 485,971 views 3 years ago 19 minutes"}},"simpleText":"The strange cousin of the complex numbers -- the dual numbers."},"longBylineText":{"runs":[{"text":"Michael Penn","navigationEndpoint":{"clickTrackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MichaelPennMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC6jM0RFkr4eSkzT5Gx0HOAw","canonicalBaseUrl":"/@MichaelPennMath"}}}]},"publishedTimeText":{"simpleText":"3 years ago"},"viewCountText":{"simpleText":"485,971 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"19 minutes, 14 seconds"}},"simpleText":"19:14"},"navigationEndpoint":{"clickTrackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWRI6b3ylKrV97OnAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=ceaNqdHdqtg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"ceaNqdHdqtg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=71e68da9d1ddaad8 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=806250 mt=1740055497 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Michael Penn","navigationEndpoint":{"clickTrackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@MichaelPennMath","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC6jM0RFkr4eSkzT5Gx0HOAw","canonicalBaseUrl":"/@MichaelPennMath"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/9FLFQU9BbmNAHFZBGHrbSH12dJWlKhfaGltsfS5JgrVgugMMGiN78jJ-39iifZNK_3pF0UofXg=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGM=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGNA2NX2jp21o_Nx","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"485K views"}},"simpleText":"485K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CNEBEP6YBBgHIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CNEBEP6YBBgHIhMIvvrd96XSiwMVdYuMCB3DpThj","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"ceaNqdHdqtg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CNEBEP6YBBgHIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["ceaNqdHdqtg"],"params":"CAQ%3D"}},"videoIds":["ceaNqdHdqtg"]}},{"clickTrackingParams":"CNEBEP6YBBgHIhMIvvrd96XSiwMVdYuMCB3DpThj","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CNIBELlqIhMIvvrd96XSiwMVdYuMCB3DpThj"}},"popupType":"TOAST"}}]}},"trackingParams":"CNEBEP6YBBgHIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CNABENGqBRgIIhMIvvrd96XSiwMVdYuMCB3DpThj","offlineVideoEndpoint":{"videoId":"ceaNqdHdqtg","onAddCommand":{"clickTrackingParams":"CNABENGqBRgIIhMIvvrd96XSiwMVdYuMCB3DpThj","getDownloadActionCommand":{"videoId":"ceaNqdHdqtg","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CNABENGqBRgIIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGM=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtjZWFOcWRIZHF0Zw%3D%3D","commands":[{"clickTrackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGM=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CM8BEI5iIhMIvvrd96XSiwMVdYuMCB3DpThj","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGM=","hasSeparator":true}}],"trackingParams":"CMwBEKQwGAEiEwi--t33pdKLAxV1i4wIHcOlOGM=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"19 minutes, 14 seconds"}},"simpleText":"19:14"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CM4BEPnnAxgCIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"ceaNqdHdqtg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CM4BEPnnAxgCIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"ceaNqdHdqtg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CM4BEPnnAxgCIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CM0BEMfsBBgDIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CM0BEMfsBBgDIhMIvvrd96XSiwMVdYuMCB3DpThj","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"ceaNqdHdqtg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CM0BEMfsBBgDIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["ceaNqdHdqtg"],"params":"CAQ%3D"}},"videoIds":["ceaNqdHdqtg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CM0BEMfsBBgDIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"The strange cousin of the complex numbers -- the dual numbers. - 19 minutes - Go to channel - Michael Penn - 485K views - 3 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/ceaNqdHdqtg/mqdefault_6s.webp?du=3000 sqp=CMis3L0G rs=AOn4CLDjZKeTNefxwHm9yoSeZSvXXKpRLQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"E08uqG0HEOk","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/E08uqG0HEOk/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCWt66H3x4DF4tMNZrNBFBPjWAkVw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/E08uqG0HEOk/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLCm22CKoHPE7fDbz2mTDL5O1R6zjQ","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Complex Numbers in 20 minutes ✅ by Transcended Institute 13,848 views 10 months ago 23 minutes"}},"simpleText":"Complex Numbers in 20 minutes ✅"},"longBylineText":{"runs":[{"text":"Transcended Institute","navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@TRANSCENDEDINSTITUTE","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCtnhi-thT_BkMF3Z71QdDHA","canonicalBaseUrl":"/@TRANSCENDEDINSTITUTE"}}}]},"publishedTimeText":{"simpleText":"10 months ago"},"viewCountText":{"simpleText":"13,848 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"23 minutes, 34 seconds"}},"simpleText":"23:34"},"navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWRI6b3ylKrV97OnAZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=E08uqG0HEOk","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"E08uqG0HEOk","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr3---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 id=134f2ea86d0710e9 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=806250 mt=1740055497 oweuc="}}}}},"shortBylineText":{"runs":[{"text":"Transcended Institute","navigationEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGMyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@TRANSCENDEDINSTITUTE","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UCtnhi-thT_BkMF3Z71QdDHA","canonicalBaseUrl":"/@TRANSCENDEDINSTITUTE"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/LR3gYzrxnOztxja-E25_qsPxSkz5Hh1rEQbPtMFR22Y7Hv8pN_hhksgLGkcfw9FO1Eikb2Kon3Y=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGNA6aGc6IbVy6cT","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"13K views"}},"simpleText":"13K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMoBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMoBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"E08uqG0HEOk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMoBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["E08uqG0HEOk"],"params":"CAQ%3D"}},"videoIds":["E08uqG0HEOk"]}},{"clickTrackingParams":"CMoBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMsBELlqIhMIvvrd96XSiwMVdYuMCB3DpThj"}},"popupType":"TOAST"}}]}},"trackingParams":"CMoBEP6YBBgFIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CMkBENGqBRgGIhMIvvrd96XSiwMVdYuMCB3DpThj","offlineVideoEndpoint":{"videoId":"E08uqG0HEOk","onAddCommand":{"clickTrackingParams":"CMkBENGqBRgGIhMIvvrd96XSiwMVdYuMCB3DpThj","getDownloadActionCommand":{"videoId":"E08uqG0HEOk","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CMkBENGqBRgGIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGM=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtFMDh1cUcwSEVPaw%3D%3D","commands":[{"clickTrackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGM=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CMgBEI5iIhMIvvrd96XSiwMVdYuMCB3DpThj","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGM=","hasSeparator":true}}],"trackingParams":"CMUBEKQwGAIiEwi--t33pdKLAxV1i4wIHcOlOGM=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"23 minutes, 34 seconds"}},"simpleText":"23:34"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMcBEPnnAxgBIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"E08uqG0HEOk","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CMcBEPnnAxgBIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"E08uqG0HEOk"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMcBEPnnAxgBIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CMYBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMYBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"E08uqG0HEOk","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMYBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["E08uqG0HEOk"],"params":"CAQ%3D"}},"videoIds":["E08uqG0HEOk"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CMYBEMfsBBgCIhMIvvrd96XSiwMVdYuMCB3DpThj"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Complex Numbers in 20 minutes ✅ - 23 minutes - Go to channel - Transcended Institute - 13K views - 10 months ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/zHNXTqe6Aqk/hqdefault.jpg?sqp=-oaymwEwCKgBEF5IWvKriqkDIwgBFQAAiEIYAfABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLC_t9G2WMl4y2xV0bBHAEwNFYa_jA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/zHNXTqe6Aqk/hqdefault.jpg?sqp=-oaymwExCNACELwBSFryq4qpAyMIARUAAIhCGAHwAQH4Af4JgALQBYoCDAgAEAEYZSBlKGUwDw== rs=AOn4CLDy37LdH4is_P1VjOLne5D6wcmauA","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"34 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4144959,"darkTheme":4144959}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Linear Algebra"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"Einstein’s Mechanics

#############################