Question

Simplify the following and express in the form a + ib:

(1 + 3i)² (3 + i)

Answer 1

(1 + 3i)² (3 + i)
= (1 + 6i + 9i²)(3 + i)
= (1 + 6i – 9)(3 + i)        ...[∵ i² = – 1]
= (– 8 + 6i)(3 + i)
=  – 24 – 8i + 18i + 6i²
= – 24 + 10i +6(– 1)
= –24 + 10i – 6
= – 30 + 10i