How Do You Prove DeMoivre's Theorem for Complex Numbers?

[lostNfound]

I think I got it

 

[LCKurtz]

Start by writing (1+i)ⁿ in trigonometric form.

What theorem do you have about raising a complex number in trigonometric form to the nth power?

 

[lostNfound]

I think I got it

 

[LCKurtz]

Start by writing (1+i)ⁿ in trigonometric form.

What theorem do you have about raising a complex number in trigonometric form to the nth power?

I did try putting (1+i)^n in trigonometric form and I got the following:
2^(n/2)*(cos(45*n)+i*sin(45*n))

OK. Now what about the answer to my question? What theorem do you have...? Look in your book.

 

[lostNfound]

DeMoivre' Thm