Question

Just need some homework help please.
Find the polar for of the following complex number: sqrt3 - sqrt3i.
I believe the answer is 3(cos pi/4 + i sin pi/4), am I correct?

Answer 1

angle should be either \(-\frac{\pi}{4}\) or \(\frac{7\pi}{4}\)

Answer 2

absolute value is
\[\sqrt{\sqrt{3}^2+\sqrt{3}^2}\]
\[=\sqrt{3+3}=\sqrt{6}\]

Answer 3

the other answer options I have are 6(cos 7pi/4 + i sin 7pi/4)
sqrt6(cos 7pi/4 - i sin 7pi/4)
and sqrt6(cos 7pi/4 + i sin 7pi/4)
I thought I worked it out correctly, guess not.

Answer 4

it is the last one

Answer 5

it helps to know what quadrant you are in so you can find the angle more easily
\(\frac{\pi}{4}\) would put you in quadrant 1 but you are in quadrant 4

Answer 6

Yes, after seeing what you wrote I guess so. Thank you for that.

Answer 7

yw
oh and don't forget \(|a+bi|=\sqrt{a^2+b^2}\)