If (1+i/1-i)3 - (1-i/1+i)3 = x+iy, then find (x,y) - Maths - Complex Numbers and Quadratic Equations

Question

If (1+i/1-i)3 - (1-i/1+i)3 = x+iy, then
find (x,y)

A K Daya Sir · Accepted Answer

(1+i/1-i)3 - (1-i/1+i)3
RATIONALIZING DENOMINATORS
[ (1 + i)2 / (1 - i2 ) ]3 - [
(1 - i)2 / (1 - i2 ) ]3
(2i/2)3 - (-2i/2)3
i3 - (-i)3
i3 + i3 = 2i3 =
2i(i2) = -2i
x + iy = -2i
x =0
y = -2