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Question
Evaluate: (1 + i)6 + (1 – i)3
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Solution
(1 + i)6 = {(1 + i)2}3
= (1 + i2 + 2i)3
= (1 – 1 + 2i)3
= 8i3
= –8i
And (1 – i)3 = 1 – i3 – 3i + 3i2
= 1 + i – 3i – 3
= –2 – 2i
Therefore, (1 + i)6 + (1 – i)3
= –8i – 2 – 2i
= –2 – 10i
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