Which of the following is a solution of z^5 = 1 + √3 i?

5√2 (cos150° + isin150°)
5√2 (cos156° + isin156°)
5√2 (cos174° + isin174°)
5√2 (cos204° + isin204°)

show me how to work it out.

Option 2 is right

Step-by-step explanation:

Given that

We can write this in polar form with modulus and radius

Hence angle = 60 degrees and

Since we have got 5 roots for z, we can write 60, 420, 780, etc. with periods of 360

Using Demoivre theorem we get 5th root would be

5th root of 2 multiplied by 1/5 th of 60, 420, 780,....

Out of these only 2nd option suits our answer

Hence answer is Option 2.

angle efh= angle egh