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?

Vinculum Jun 9, 2022

#2**+3 **

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.

Melody Jun 9, 2022