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Question

If a2+b2=1, then 1+b+ia1+bia=

A
1
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B
2
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C
b + ia
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D
a + ib
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Solution

The correct option is C b + ia
Given that a2+b2=1
1+b+ia1+bia=(1+b+ia)(1+b+ia)(1+bia)(1+b+ia)
=(1+b)2a2+2ia(1+b)1+b2+2b+a2
=(1a2)+2b+b2+2ia(1+b)2(1+b)
=2b2+2b+2ia(1+b)2(1+b)=b+ia

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