Question

If z is a complex number of unit modulus and argument q, then `a r g((1+z)/(1+ bar z))` equal (1) `pi/2-theta` (2) `theta` (3) `pi-theta` (4) `-theta`
A. `- theta `
B. `pi/2- theta`
C. ` theta`
D. `pi - theta`

Answer 1

Correct Answer - C
Given |z| =1 arg z= `theta` :. Z = `e^itheta`
`therefore barz =e^(-itheta)rArr bar z = 1/z`
`therefore arg (1+z)/(1+z)=arg (1+z/1+1/z)=arg (z)= theta`