Question

If z is a complex number $\overline{z^{-1}}\left(\overline{z}\right)$ = , then

• A. 1
• B. -1
• C. 0
• D. None of these

Answer 1

The correct option is A

1

Let z = x + iy, $\overline{z}$ = x -iy and $z^{-1}=\frac{1}{x+iy}$

⇒ $\overline{z^{-1}}=\frac{x+iy}{x^2+y^2}$ ; ∴ $\overline{z^{-1}}\overline{z}=\frac{x+iy}{x^2+y^2}(x-iy)$ = 1