Π£ Π½Π°Ρ Π²Ρ ΠΌΠΎΠΆΠ΅ΡΠ΅ ΠΏΠΎΡΠΌΠΎΡΡΠ΅ΡΡ Π±Π΅ΡΠΏΠ»Π°ΡΠ½ΠΎ ΠΡΠ½ΠΎΠ²Ρ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΡΡ ΡΠΈΡΠ΅Π» | ΠΠΏ. 3 ΠΠΈΠ²Π°Ρ ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΠΊΠ° Π±Π»ΠΎΠΊΠΈΡΠΎΠ²ΠΊΠΈ ΠΈΠ»ΠΈ ΡΠΊΠ°ΡΠ°ΡΡ Π² ΠΌΠ°ΠΊΡΠΈΠΌΠ°Π»ΡΠ½ΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ½ΠΎΠΌ ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅, ΠΊΠΎΡΠΎΡΠΎΠ΅ Π±ΡΠ»ΠΎ Π·Π°Π³ΡΡΠΆΠ΅Π½ΠΎ Π½Π° ΡΡΡΠ±. ΠΠ»Ρ ΡΠΊΠ°ΡΠΈΠ²Π°Π½ΠΈΡ Π²ΡΠ±Π΅ΡΠΈΡΠ΅ Π²Π°ΡΠΈΠ°Π½Ρ ΠΈΠ· ΡΠΎΡΠΌΡ Π½ΠΈΠΆΠ΅:
ΠΡΠ»ΠΈ ΠΊΠ½ΠΎΠΏΠΊΠΈ ΡΠΊΠ°ΡΠΈΠ²Π°Π½ΠΈΡ Π½Π΅
Π·Π°Π³ΡΡΠ·ΠΈΠ»ΠΈΡΡ
ΠΠΠΠΠΠ’Π ΠΠΠΠ‘Π¬ ΠΈΠ»ΠΈ ΠΎΠ±Π½ΠΎΠ²ΠΈΡΠ΅ ΡΡΡΠ°Π½ΠΈΡΡ
ΠΡΠ»ΠΈ Π²ΠΎΠ·Π½ΠΈΠΊΠ°ΡΡ ΠΏΡΠΎΠ±Π»Π΅ΠΌΡ ΡΠΎ ΡΠΊΠ°ΡΠΈΠ²Π°Π½ΠΈΠ΅ΠΌ, ΠΏΠΎΠΆΠ°Π»ΡΠΉΡΡΠ° Π½Π°ΠΏΠΈΡΠΈΡΠ΅ Π² ΠΏΠΎΠ΄Π΄Π΅ΡΠΆΠΊΡ ΠΏΠΎ Π°Π΄ΡΠ΅ΡΡ Π²Π½ΠΈΠ·Ρ
ΡΡΡΠ°Π½ΠΈΡΡ.
Π‘ΠΏΠ°ΡΠΈΠ±ΠΎ Π·Π° ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ ΡΠ΅ΡΠ²ΠΈΡΠ° savevideohd.ru
Intro to the geometry complex numbers. Full playlist: Β Β Β β’Β LockdownΒ mathΒ Β Home page: https://www.3blue1brown.com Brought to you by you: https://3b1b.co/ldm-thanks Beautiful pictorial summary by @ThuyNganVu: Β Β /Β 1258219199769440257Β Β Errors: - On the first sketch of a complex plane, there is a "2i" written instead of "-2i". - At the end, in writing the angle sum identity, the last term should be sin(beta) instead of sin(alpha). - During Q9, the terms in parentheses should include an i, (1/2 + sqrt(3)/2 i) Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld ------------------ The live question setup with stats on-screen is powered by Itempool. https://itempool.com/ The graphing calculator used here is Desmos. https://www.desmos.com/ The "Complex slide rule" came from Geogebra, via Ben Sparks. https://www.geogebra.org/m/mbhbdvkr Curious about other animations? https://www.3blue1brown.com/faq#manim Music by Vincent Rubinetti. Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/a... Stream the music on Spotify: https://open.spotify.com/album/1dVyjw... If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. ------------------ Video Timeline (thanks to user "Just TIEriffic") 0:00:30 - W3 Results 0:01:00 - W4 Prompt 0:02:00 - Ask What would you call 'imaginary numbers'? 0:06:40 - Startingpoint & assumptions 0:10:25 - W4 Results 0:11:25 - Q1 Prompt 0:12:20 - Q1 Process 0:14:05 - RotatingCoordinates 0:16:40 - Q1 Result 0:17:40 - Q2 0:18:15 - Q3 Prompt 0:19:40 - Q3 Results 0:21:35 - RotationAnimation 0:22:35 - 3 facts about Multiplication 0:25:40 - Q4 Prompt 0:26:10 - Ask imaginary I vs physics i&j 0:28:15 - Q4 Result 0:31:00 - GeoGebraDemo 0:32:10 - Q5 Prompt 0:33:30 - Q5 Results 0:34:00 - Q5 Solution 0:35:55 - RotatingImages Example 0:37:10 - PythonExample 0:38:25 - PythonImage Rotation Example 0:40:35 - Ask Vectors & Matrices for rotation 0:42:40 - Q6 Prompt 0:46:55 - Q6 Results 0:47:25 - Q6 Solution 0:52:20 - RedefiningAngle Addition 0:57:20 - Q7 Prompt 0:57:55 - Ask Can we do without complex numbers? 1:00:10 - Q7 Results 1:00:55 - Q7 Solution 1:05:45 - Q8 Prompt 1:06:30 - Ask sum/difference of angles 1:09:25 - Q8 Results 1:10:25 - Q8 Solution 1:12:00 - DesmosExample 1:15:05 - Bringing it all together 1:16:25 - The "cis" shorthand explained 1:18:05 - Q9 Prompt 1:19:35 - Q9 Results 1:20:55 - ClosingRemarks ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: Β Β /Β 3blue1brownΒ Β Reddit: Β Β /Β 3blue1brownΒ Β Instagram: Β Β /Β 3blue1brown_animationsΒ Β Patreon: Β Β /Β 3blue1brownΒ Β Facebook: Β Β /Β 3blue1brownΒ Β