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Hi Amit,
The answer is (d) - none of these.
x = z/conj(z) = (x + iy)/(x - iy)
x = (x+iy)2/(x-iy)(x+iy) ( Multiplying Nr and Dr by x + iy )
= ( x2 - y2 + 2ixy ) / ( x2 + y2 )
Modulus of x = Root [((x2 - y2)/( x2 + y2 ))2 + (2xy)2/( x2 + y2 )2]
= 1/( x2 + y2 )*Root(x4 + y4 -2x2y2 + 4x2y2)
= 1/( x2 + y2 )*Root( x4 + y4 + 2x2y2 )
= 1/( x2 + y2 )*Root(( x2 + y2)2)
= 1/( x2 + y2 )*( x2 + y2 )
= 1
Hence Answer is (d)
Please feel free to ask as many questions as you have.
Puneet
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