Basic complex analysis | Imaginary and complex numbers | Precalculus | Khan Academy

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Argand Diagram, magnitude, modulus, argument, exponential form

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i = rotation by 90 deg.

i x i = rotation by 180 deg.

i x i x i = rotation by 270 deg.

Complex numbers are used to indicate rotation.

Hope this helps.

Binnoy
Visualizing Maths
A book beyond formulas

Dedicated to you and all such similar minds searching for answers.

Visualizingmathandphysics
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Want an algebraic vector to play with?
[(x-1)/(x+3), (x+2-i*x)/(x+3), (x+2+i*x)/(x+3)]
The distance is 1.

thomasolson
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Just to be in the safe side, this is done in Argand diagram right?

MrYounis
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I dont know how to put this, but the timing of this video is *spot* on, just before my terminal exams. Thanks!

Krabby_Patty
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i thought i^2 was -1? or are you taking the absolute value of it cause of the distance thing

visiting
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No because if you think about the Pythagorean Theorem:

c^2 = a^2 + b^2

Well, we are looking for the magnitude of the complex number, or in other words it's radius.

r^2 = a^2 + b^2
Therefore
r = Sqrt( a^2 + b^2 )
or
|z| = Sqrt( a^2 + b^2 )
|z| = Sqrt( 3/4 + 1/4 )

HellaPerformance
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I have watched several of your videos, several of your videos and they are wonderful, they are wonderful.

patrickoneillnl
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Sqrt( 1 ) = + or - 1..

The reason he chooses one in this scenario though is because he is looking for the length of the modulus. As Klatjofsky put it, lengths are always positive.

HellaPerformance
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Please start a series on COMPLEX ANALYSIS.

koushikghosh
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Thank you sir, now I'm ready for my quiz on complex numbers 💯

Motivationtosuccess-qsih
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Excellent explanation of the complex number. Thank you, indeed.

fahmylina
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You are great SIR. Thank you for your online lesson.

debajyotibhattacharjee
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Yes, but remember that he's trying to figure out the length of the position vector and lengths are always positive :)

Klatjofsky
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Thank you so much! I don't know how many times you've heard this but you've seriously helped us. :D

anonymousL
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this is so easy, we want real analysis complex

mouadovic
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what an amazing video. really helped me a lot

thank you and as a muslim May Allah guide you to his way. :P

salaheamean
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at 10:07, why did you square the denominator from 2 to 4?

thetempest
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thanks so much for this video~!!!
nice visual presentation and made a lot of things clearer :D

missAyzl
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Complex numbers indicate rotation.

In maths, the number '1' indicates 'as it is'

The number 'i' indicates 'rotated by 90 deg'

The number '-1' indicates 'rotated by 180 deg'.

The number '-i' indicates 'rotated by 270 deg'.

Binnoy
Visualizing maths
A book beyond formulas
Dedicated to you and such similar minds searching for answers.

Visualizingmathandphysics
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Really good video, this was my first introduction to the complex analysis and it makes me want to learn a lot more about it =)

Aurelien