Find the value of following expression:
(1 + i)6 + (1 – i)3
(1 + i)6 + (1 – i) 3 = {(1 + i)2 }3 + (1 – i)2 (1 – i)
= {1 + i2 + 2i}3 + (1 + i2 – 2i)(1 – i)
= {1 – 1 + 2i}3 + (1 – 1 – 2i)(1 – i)
= (2i)3 + (– 2i)(1 – i)
= 8i3 + (– 2i) + 2i2
[since i3 = – i, i2 = – 1]
= – 8i – 2i – 2
= – 10 i – 2
= – 2(1 + 5i)