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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Complex Number

JEE Main 2020 · 6 September · Evening Shift · Mathematics · Complex Number

Let z = x + iy be a non-zero complex number such that z ^ 2 = i |z|...

Let z=x+iyz = x + iy be a non-zero complex number such that z2=i∣z∣2{z}^{2} = i{\left|z\right|}^{2}, where i=−1i = \sqrt{- 1}, then zz lies on the :

Options

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

Correct answer

C. line, y=xy = x

Step-by-step solution

(x+iy)2=i(x2+y2){\left(x + iy\right)}^{2} = i\left({x}^{2} + {y}^{2}\right)

⇒x2−y2+2ixy=i(x2+y2)⇒ {x}^{2} - {y}^{2} + 2ixy = i ( {x}^{2} + {y}^{2} )

compare real and imaginary parts

⇒x=y⇒ x = y

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