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Find the value of i49 + i68 + i89 + i110 - Mathematics and Statistics

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Sum

Find the value of i49 + i68 + i89 + i110 

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Solution

i49 + i68 + i89 + i110 
= (i4)12 .i + (i4)17 + (i4)22 .i + (i4)27 .i2
= (1)12 .i + (1)17 + (1)22 .i + (1)27 (– 1)    ...[∵ i4 = 1, i2 = – 1]
= i + 1 + i – 1
= 2i

Concept: Algebra of Complex Numbers
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