What are the five values of (1+i√3)^(3/5)?

[juliany]

Homework Statement

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) ?

 

[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 $$1+i\sqrt{3}=-2$$