Question

find the trigonometric form of -5+5i

Answer 1

Ewh

Answer 2

first you need
\(r=\sqrt{a^2+b^2}\)

Answer 3

in your case it is \(\sqrt{5^2+5^2}=\sqrt{50}=2\sqrt{5}\)

Answer 4

That's the modulus, or the r part of the rcistheta

Answer 5

Next, we find the angle, or the theta part of the rcistheta

Answer 6

then you need \(\theta\) and you have to be careful here because while it is true that \(\tan(\theta)=\frac{b}{a}\) it is not necessarily true that \(\theta=\tan^{-1}\frac{b}{a}\)

Answer 7

from the picture (and you should draw one before you do this) you can see that \(\theta=\frac{3\pi}{4}\)

Answer 8

if you take out your calculator and find \(\tan^{-1}(-1)\) you will get \(-\frac{\pi}{4}\) or maybe \(-45\) but that is the wrong angle because you are in quadrant 2 and not in quadrant 4

Answer 9

right

Answer 10

it would be 135degrees and 3pi4

Answer 11

yes