Let z 1 and z 2 be two complex numbers such that z ¯ 1 = i z ¯ 2 and arg z 1 z ¯ 2 = π ,…

Let z1 and z2 be two complex numbers such that z¯1=iz¯2 and argz1z¯2=π, then the argument of z1 is
  1. arg z2=π4
  2. arg z2=-3π4
  3. arg z1=π4
  4. arg z1=-3π4

Solution

z¯1=iz¯2  ⇒z1=-iz2  ⇒iz1=z2⇒eiπ2z1=z2

Given, argz1z¯2=π

Let z1=reiθ   ⇒  z2¯=re-iπ2+θ

So argei2θ+π2=π   ⇒  2θ+π2=π
⇒   θ=π4

Asked in: JEE Main 2022 (25 Jun Shift 2)

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