Prove type question.

Asked by impuranik | 10th Sep, 2010, 02:30: PM

Expert Answer:

a + ib = (x + i)2/(2x2+1)
a + ib = (x2 + 2xi - 1)/(2x2+1)
Equating the real and imagnary parts, we get,
a = (x2 - 1)/(2x2+1)
b = 2x /(2x2+1)
Hence,
a2 + b2 = (x2 - 1)2/(2x2+1)2 + 4x2 /(2x2+1)2
a2 + b2 = (x4 - 2x2 + 1 + 4x2)/(2x2+1)2
a2 + b2 = (x4 + 2x2 + 1 )/(2x2+1)2
a2 + b2 = (x2 + 1 )2/(2x2+1)2
regards,
Team,
TopperLearning.

Answered by  | 10th Sep, 2010, 04:13: PM

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