Expand (3+i)^5, where i^2=-1
(3+i)^5=?
Please and thanks.
shifting to polar..
3+i= sqrt10 @arctan(1/3) on the complex plane
so
(3+i)^5=(sqrt10)^2 @5*arctan(1/3)
and that is
100sqrt10 @5*18.4349488deg
100sqrt10 @92.17 deg
converting back to complex plane
real+ imag where
real=100Sqrt10*cos91.17
imag=i*100sqrt10*sin91.17