Q1 of 202 Page 171

Simplify each of the following and express it in the form a + ib :
2(3 + 4i) + i(5 – 6i)

Given: 2(3 + 4i) + i(5 – 6i)

Firstly, we open the brackets

2 × 3 + 2 × 4i + i × 5 – i × 6i

= 6 + 8i + 5i – 6i²

= 6 + 13i – 6(-1) [∵, i² = -1]

= 6 + 13i + 6

= 12 + 13i

Prove that n N.

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

(–5 + 6i) – (–2 + i)

Simplify each of the following and express it in the form a + ib :2(3 + 4i) + i(5 – 6i)