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Question

If x+iy=a+ibaib, prove that x2+y2=1

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Solution

x+iy=a+ibaib
|x+iy|=a+ibaib (Taking modulus on both sides)
|x+iy|=|a+ib||aib| [z1z2=|z1||z2|]
x2+y2=a2+b2a2+(b)2
x2+y2=(a2+b2)(a2+b2)
x2+y2=1
Hence Proved

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