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Question
Simplify the following and express in the form a + ib:
(1 + 3i)2 (3 + i)
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Solution
(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
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