Question

Help please!! Fan and medal :)
Which expression is a fourth root of -1+isqrt(3)?
I will attach a photo of the answers

Answer 1

@math&ing001 Can you help me again?

Answer 2

Let the answer be x+iy.
\[(x+iy)^{^{2}}=-1+\sqrt{3}i\]

Answer 3

-1+i*sqrt(3) = 2(-1/2 + i*sqrt(3)/2) = 2exp(i*2pi/3)
Now apply the fourth root and see what you get.

Answer 4

Sorry its raised to the fourth power

Answer 5

I'm sorry but I'm extremely confused by both of your explanations.... @Prathamesh_M I'm supposed to be converting to polar form I believe... and @math&ing001 I don't understand the formatting by which you are trying to teach me.

Answer 6

polar form means cos theta + i(sin theta) right?

Answer 7

Yes @Prathamesh_M

Answer 8

in that case u can always find the answer in terms of x + iy and then find the cos inverse of x and the sin inverse of y

Answer 9

If you haven't seen the exponential form you can use this
-1+i*sqrt(3) = 2(-1/2 + i*sqrt(3)/2) = 2(cos(3pi/2)+i*sin(3pi/2))
And use De Moivre's formula like you did before.

Answer 10

my method would be awfully long but it should work

Answer 11

\[(\cos(x)+i \sin(x))^{1/4} = \cos(x/4)+i \sin(x/4)\]

Answer 12

Hi, sorry @math&ing001... I'm confused as to where you got the x/4??

Answer 13

I just used De Moivre's theorem for n=1/4
You can check it here https://en.wikipedia.org/wiki/De_Moivre's_formula

Answer 14

So the answer would be 4sqrt(2)(cos(30)+isin(30)) right? @math&ing001

Answer 15

Yes, correct !

Answer 16

It was correct, thanks! :) @math&ing001

Answer 17

Welcome =)