if x=z/conj(z) then/x/ equal (A) 0 (B) -1 (C) i (D) none of these

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