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AP EAMCET20227 Jul 2022Evening ShiftMathematicsComplex NumberActual

Let z and w be two distinct non-zero complex numbers if |z|^2 w-|w|^2 z=z-w , then

Options

  1. Aw= z ^2
  2. Bz W =2
  3. Cz W =1
  4. DW= Z

Correct answer

C. z W =1

Step-by-step solution

array ll & (|z|^2+1 ) w= (|w|^2+1 ) z & Let z=k w, k 1, k 0 & k^2|w|^2 w-k|w|^2 w=k w-w & k|w|^2 w(k-1)=(k-1) w & k= 1 |w|^2 & z= w |w|^2 & z w = w |w|^2 w = |w|^2 |w|^2 =1 array

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