Verified Solution • 2025–26 Session moderate

QJEEM22Ma7eef: JEE Main 2022 Mathematics - Class 11 JEEM22Ma7eef Solution: Let z 1 and z 2 be two complex numbers such that and . Then :

Let z1 and z2 be two complex numbers such that z‾1=iz‾2{\overline z _1} = i{\overline z _2} and arg⁡(z1z‾2)=π\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi . Then :

Multiple Choice Options

  • A arg⁡z2=π4\arg {z_2} = {\pi \over 4}
  • B arg⁡z2=−3π4\arg {z_2} = - {{3\pi } \over 4}
  • C arg⁡z1=π4\arg {z_1} = {\pi \over 4}
  • D arg⁡z1=−3π4\arg {z_1} = - {{3\pi } \over 4}

Step-by-Step Verified Solution

∵\because z1z2=−i⇒z1=−iz2{{{z_1}} \over {{z_2}}} = - i \Rightarrow {z_1} = - i{z_2}

⇒arg⁡(z1)=−π2+arg⁡(z2)\Rightarrow \arg ({z_1}) = - {\pi \over 2} + \arg ({z_2}) ..... (i)

Also arg⁡(z1)−arg⁡(z‾2)=π\arg ({z_1}) - \arg ({\overline z _2}) = \pi

⇒arg⁡(z1)+arg⁡(z2)=π\Rightarrow \arg ({z_1}) + \arg ({z_2}) = \pi ..... (ii)

From (i) and (ii), we get

arg⁡(z1)=π4\arg ({z_1}) = {\pi \over 4} and arg⁡(z2)=3π4\arg ({z_2}) = {{3\pi } \over 4}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring