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# Question

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I have a question, how do you find the magnitude of a point on a complex plane?

For example something like this:

I know the point would be something like 2+(3pi/4)I think.

But how would I find the magnitude?

Jun 9, 2022

#1
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Magnitude  of  a ±  bi =

sqrt  [ a^2  + b^2 ]

Jun 9, 2022
#2
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The magnitude of a point on the complex plane is just the distance of that point to the 0.   (the origin)

That is why the symbol used is the same as the absolute sign.

In your case  |w|=2   assuming that each of those arcs is 1 unit apart

I would assume that that point is

$$2e^{(\frac{3\pi}{4}i)} \\= 2cis(\frac{3\pi}{4})\\= 2[cos(\frac{3\pi}{4})+isin(\frac{3\pi}{4})]\\ =2[-\frac{1}{\sqrt2}+i*\frac{1}{\sqrt2}]\\ =\sqrt2[-1+i]\\$$

what CPhill has written is also correct.

Jun 9, 2022
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(deleted)

I got it, Thank you

Vinculum  Jun 9, 2022
edited by Vinculum  Jun 9, 2022
edited by Vinculum  Jun 9, 2022
#3
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Ohhhh I got it!!!

Thank you CPhill and Melody I think I understand it now.

Jun 9, 2022
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Its basically just the Pythagorean Theorem(somebody spellcheck that) i don't think that the fact that it is on a complex plane matters :) just like what CPhill said
Jun 9, 2022
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i am very late to this question
Hamburger  Jun 9, 2022