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JEE Main20206 Sep 2020Evening ShiftMathematicsComplex NumberActual

Let z = x + iy be a non-zero complex number such that z 2 = i z 2 , where i = - 1 , then z lies on the :

Options

  1. Aline, y = - x
  2. Bimaginary axis
  3. Cline, y = x
  4. Dreal axis

Correct answer

C. line, y = x

Step-by-step solution

x + i y 2 = i x 2 + y 2 ⇒ x 2 - y 2 + 2 i x y = i ( x 2 + y 2 ) compare real and imaginary parts ⇒ x = y

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