Complex Numbers Question

[juliany]

1. The problem statement, all variables and given/known data
Find the five values of (1+i√3)^(3/5)

This question was from my recent end of year exam, I hadn't come across a question like it in my revision, does it mean find the five roots of (1+i√3)^(3/5) ?:confused:

[vela]

You want to find the five 5th roots of (1+i√3)3.

[Outlined]

you want to find all the solutions of the equation X5 = (1 + i√3)3 = -8.

[HallsofIvy]

It's remarkable that the third power is equal to -8!!

Yes, you can find the five fifth roots of (1+i\sqrt{3})^3 or just apply D'Moivre's theorem to 1+ i\sqrt{3} with n= 3/5.

[Outlined]

It's remarkable that the third power is equal to -8!!

why?

[Mentallic]

Because it's a real number. (-2)3=-8 as well so some might be reluctant enough to say that 1+i\sqrt{3}=-2 :tongue: