Consider the following in respect of a complex number Z : 1. (Z⁻¹ ) =( Z )⁻¹ 2. Z Z⁻¹=|Z|^2 Which of the above is/are correct?

Step-by-step solution

Let z=x+i y, z =x-i y and z⁻¹= 1 z = 1 x+i y 1. ( z⁻¹ )= ( 1 x+i y )= ( x-i y x^2+y^2 )= ( x+i y x^2+y^2 ) aligned & ( z )⁻¹=(x-i y)⁻¹= 1 x-i y = x+i y x^2+y^2 & ( z⁻¹ )=( z )⁻¹ aligned 2. z z⁻¹=(x+i y) ( 1 x-i y )= (x+i y)(x+i y) (x-i y)(x+i y) = (x+i y)^2 x^2+y^2 =|z|^2 Hence, both (1) and (2) are true.