Verified Solution • 2025–26 Session moderate

QJEEM20Ma6a85: JEE Main 2020 Mathematics - Class 11 JEEM20Ma6a85 Solution: Let z = x + iy be a non-zero complex number such that , where i …

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

Multiple Choice Options

  • A line, y = –x
  • B real axis
  • C line, y = x
  • D imaginary axis

Step-by-Step Verified Solution

Given z = x + iy

and z2=i∣z∣2{z^2} = i{\left| z \right|^2}

⇒\Rightarrow (x + iy)2 = i(x2 + y2)

⇒\Rightarrow x2 - y2 + 2ixy = i(x2 + y2) + 0

Comparing both side we get,

x2 - y2 = 0

⇒\Rightarrow x2 = y2

and 2xy = (x2 + y2)

⇒\Rightarrow (x - y)2 = 0

⇒\Rightarrow x = y

∴\therefore z lies on line x = y

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