Question

Find all the complex fourth roots of z=-10,000.
Write each root in standard polar form with the argument in radians.

Answer 1

@Loser66

Answer 2

easiest to find the fourth roots of \(-1\) and then multiply them all by \(10\)

Answer 3

that is supposed to represent the unit circle in the complex plane
\(-1\) is indicated
take one fourth of the angle, which is \(\pi\) and get \(\frac{\pi}{4}\) to find the first fourth root

Answer 4

that one is \(\frac{\sqrt2}{2}+\frac{\sqrt2}{2}i\)

Answer 5

others are evenly spaced bout the unit circle, and they should be easy to find

Answer 6

multiply all by \(10\) and you are done

Answer 7

oh i forgot this rather unnecessary instruction
Write each root in standard polar form with the argument in radians.
first one is either
\[10e^{\frac{\pi}{4}i}\] or
\[10\left(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4})\right)\]

Answer 8

wow. you made that so simple to understand, thank you so much!

Answer 9

yw
it is really really easy, which is the reason that you would write a complex number in polar form to begin with, to work with the angles

Answer 10

r ^6 = -1 , work with it, please.