Question

4th root of 1/2 - sqrt3/2(i)

Answer 1

0.5 - 0.866025404 i

Answer 2

can you tell me how you did it please?

Answer 3

I think you are looking for something else

Answer 4

\[\text{ Let } x=\frac{1}{2}-\frac{\sqrt{3}}{2}i \]
first let's write this number in trigonometric form

Answer 5

do you know how to do that

Answer 6

hint the form that I seek is
\[x=\cos(\theta)+\sin(\theta) i\]

Answer 7

can you give me a sec

Answer 8

k

Answer 9

i am trying to do it on paper sorry DX

Answer 10

you can use the unit circle

Answer 11

when is cosine 1/2 and sine -sqrt(3)/2

Answer 12

On my test in school, my teacher doesn't allow us to use the unit circle so i am trying to remember it by memories

Answer 13

so would it be cos(5pi/3)+isin(5pi/3)?

Answer 14

coolness

Answer 15

\[x=\cos( \frac{5\pi}{3}+2n \pi)+i \sin(\frac{5\pi}{3}+2n \pi) \\ x=e^{i (\frac{5 \pi}{3} +2 n \pi)} \\ x^\frac{1}{4}=e^{\frac{i}{4}( \frac{5\pi}{3}+2 n \pi)} \\ \]
you want 4 numbers
so n=0 will give you one
n=1 gives you another
n=2 gives you your 3rd one
and finally n=3 gives you your last 4th root