Q1 of 202 Page 171

Simplify each of the following and express it in the form a + ib :
(3 + 4i) (2 – 3i)

Given: (3 + 4i) (2 – 3i)

Firstly, we open the brackets

3 × 2 + 3 × (-3i) + 4i × 2 – 4i × 3i

= 6 – 9i + 8i – 12i²

= 6 – i – 12(-1) [∵, i² = -1]

= 6 – i + 12

= 18 – i

Simplify each of the following and express it in the form a + ib :

(1 – i)² (1 + i) – (3 – 4i)²

Simplify each of the following and express it in the form a + ib :

Simplify each of the following and express it in the form (a + ib) :

Simplify each of the following and express it in the form a + ib :(3 + 4i) (2 – 3i)