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Question

If 1-ix1+ix=a+ib, then a2+b2=
(a) 1
(b) −1
(c) 0
(d) none of these

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Solution

(a) 1

1-ix1+ix = a+ibTaking modulus on both the sides, we get:1-ix1+ix = a+ib12+x212+x2= a2+b2a2+b2 = 1Squaring both the sides, we get: a2+b2 = 1

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