Question
If z is a complex number such that z^ 2 =( z )^ 2 , then
BITSAT
Mathematics
Complex Number
2021
BITSAT 2021
BITSAT Mathematics Question (2021) — Solution
Options
- A. z is purely real
- B. z is purely imaginary
- C. either z is purely real or purely imaginary
- D. None of these
Answer
C. either z is purely real or purely imaginary
Step-by-step solution
Let z=x+i y, then its conjugate z =x-i y Given that z^ 2 =( z )^ 2 array l x^ 2 -y^ 2 +2 i x y=x^ 2 -y^ 2 -2 i x y \\ 4 i x y=0 array
Related: Mathematics — Complex Number · All PYQ Banks