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

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

(3 + 4i) (2 – 3i)

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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

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