How do you simplify [(3+2i)^ 3 / (-2+3i)^4] ?

1 Answer
Jun 27, 2016

(3-2i)/13

Explanation:

3+2i=sqrt(3^2+2^2)e^{i phi}
-2+3i=sqrt(3^2+2^2)e^{i( phi+pi/2)}

with phi = arctan(2/3)

[(3+2i)^ 3 / (-2+3i)^4] =((3+2i)/(-2+3i))^3/( (-2+3i))=e^{-i (3pi)/2}/(sqrt(3^2+2^2)e^{i( phi+pi/2)})
=1/sqrt(3^2+2^2)e^{-i(phi+2pi)} = 1/sqrt(3^2+2^2)e^{-i phi} =
sqrt(3^2+2^2)/(3^2+2^2)e^{-i phi} = (3-2i)/13