If Re `(lambda Z + (2)/(Z))` is zero and Re(z) `!= 0` and |Z| = 2. Then `lambda` can be

Options

A. 2
B. `-2`
C. `(1)/(2)`
D. `-(1)/(2)`

Answer

D

Explanation

Let Z = x + yi
`= lambda (x + yi) + (2(x - yi))/(x^(2) + y^(2))`
`= x lambda + (2x)/(x^(2) + y^(2)) = 0` [Re part = 0]
`= lambda = - (2)/(|z|^(2)) implies lambda = - (2)/(4), lambda = (1)/(2)`