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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 B b+ia
Given a2+b2=1

1+b+ia1+bia

=(1+b+ai)2(1+b)2+a2

=1+b2a2+2b+2iab+2ia1+b2+2b+a2

=1+b2a2+2b+2iab+2ia2+2b

=2b2+2b+2ia(1+b)2+2b

=b+ia

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