# Math

posted by Philip

Expand (3+i)^5, where i^2=-1

(3+i)^5=?

1. bobpursley

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

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