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

Argand Diagram, magnitude, modulus, argument, exponential form

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[Visualizingmathandphysics]

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.

[thomasolson]

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.

[MrYounis]

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

[Krabby_Patty]

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

[visiting]

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

[HellaPerformance]

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 )

[patrickoneillnl]

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

[HellaPerformance]

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.

[koushikghosh]

Please start a series on COMPLEX ANALYSIS.

[Motivationtosuccess-qsih]

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

[fahmylina]

Excellent explanation of the complex number. Thank you, indeed.

[debajyotibhattacharjee]

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

[Klatjofsky]

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

[anonymousL]

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

[mouadovic]

this is so easy, we want real analysis complex

[salaheamean]

what an amazing video. really helped me a lot

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

[thetempest]

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

[missAyzl]

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

[Visualizingmathandphysics]

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.

[Aurelien]

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