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

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

Grade:Upto college level

1 Answers

Puneet Mittal AskiitiansExpert-IITD
22 Points
11 years ago

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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