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BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Complex Number

BITSAT 2021 · Mathematics · Complex Number

If z is a complex number such that z^ 2 =( z )^ 2 , then

If zz is a complex number such that z2=(zˉ)2z^{2}=(\bar{z})^{2}, then

Options

  1. Azz is purely real
  2. Bzz is purely imaginary
  3. Ceither zz is purely real or purely imaginary
  4. DNone of these

Correct answer

C. either zz is purely real or purely imaginary

Step-by-step solution

Let z=x+iyz=x+i y, then its conjugate zˉ=x−iy\bar{z}=x-i y Given that z2=(zˉ)2z^{2}=(\bar{z})^{2}⇒x2−y2+2ixy=x2−y2−2ixy⇒4ixy=0\begin{array}{l} \Rightarrow x^{2}-y^{2}+2 i x y=x^{2}-y^{2}-2 i x y \\ \Rightarrow 4 i x y=0 \end{array}$$
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