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JEE Main2004MathematicsComplex NumberActual

If z=x-i y and z^ 1 3 =p+i q , then ( x p + y q ) (p^2+q^2 ) is equal to

Options

  1. A1
  2. B-2
  3. C2
  4. D-1

Correct answer

B. -2

Step-by-step solution

z=(p+i q)^3=p (p^2-3 q^2 )-i q (q^2-3 p^2 ) x p =p^2-3 q^2 & y q =q^2-3 p^2 x p + y q (p^2+q^2 ) =-2

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