OpenStudy (anonymous):

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

2 years ago
OpenStudy (candy13106):

0.5 - 0.866025404 i

2 years ago
OpenStudy (anonymous):

can you tell me how you did it please?

2 years ago
OpenStudy (freckles):

I think you are looking for something else

2 years ago
OpenStudy (freckles):

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

2 years ago
OpenStudy (freckles):

do you know how to do that

2 years ago
OpenStudy (freckles):

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

2 years ago
OpenStudy (anonymous):

can you give me a sec

2 years ago
OpenStudy (freckles):

k

2 years ago
OpenStudy (anonymous):

i am trying to do it on paper sorry DX

2 years ago
OpenStudy (freckles):

you can use the unit circle

2 years ago
OpenStudy (freckles):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (freckles):

coolness

2 years ago
OpenStudy (freckles):

\[x=\cos( \frac{5\pi}{3}+2n \pi)+i \sin(\frac{5\pi}{3}+2n \pi) \\ x=e^{i (\frac{5 \pi}{3} +2 n \pi)} \\ x^\frac{1}{4}=e^{\frac{i}{4}( \frac{5\pi}{3}+2 n \pi)} \\ \] 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

2 years ago
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