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Question
Is (1 + i14 + i18 + i22) a real number? Justify your answer
Solution
1+ i14 + i18 + i22
= 1 + (i4)3.i2 + (i4)4.i2 + (i4)5.i2
= 1+ (1)3 (–1) + (1)4 (–1) + (1)5 (–1) ...[∵ i2 = – 1, i4 = 1]
= 1 – 1 – 1 – 1
= – 2, which is a real number.
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