If z is a complex number ¯ ¯¯¯¯¯¯ ¯ z − 1 ( ¯ z ) = , then Options: A . &nbsp 1 B . &nbsp -1 C . &nbsp 0 D . &nbsp None of these

Answer: Option A : A Let z = x + iy, ¯ z = x -iy and z − 1 = 1 x + i y ⇒ ¯ ¯¯¯¯¯¯ ¯ z − 1 = x + i y x 2 + y 2 ; ∴ ¯ ¯¯¯¯¯¯ ¯ z − 1 ¯ z = x + i y x 2 + y 2 ( x − i y ) = 1

If z is a complex number ¯¯¯¯¯¯¯¯z

Discussion Forum : Complex Numbers

Question -

If z is a complex number $^{- 1} (¯ z)$ = , then

Options:

A . 1

B . -1

C . 0

D . None of these

Answer: Option A
:
A

Let z = x + iy, $¯ z$ = x -iy and $z^{- 1} = \frac{1}{x + i y}$
⇒ $^{- 1} = \frac{x + i y}{x^{2} + y^{2}}$ ; ∴ $^{- 1} ¯ z = \frac{x + i y}{x^{2} + y^{2}} (x - i y)$ = 1

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