Correct Answer - Option 3 : 5π/2
Concept:
Properties of complex numbers
z = \(\rm \overline{z}\), if z is purely real
z = - \(\rm \overline{z}\), if z is either 0 or purely imaginary
arg(zn) = n arg(z)
Calculation:
Given that
\(\rm \overline{z_{1}} - i \overline{z_{2}^{2}}\) = 0
z1 = -i z22
arg(z1) - arg(z2) = 2π
arg(-i z22) - arg(z2) = 2π
arg(-i) + arg(z22) - arg(z2) = 2π
\(\rm \frac{-π}{2} \)+ 2 arg(z2) - arg(z2) = 2π
arg(z2) = 2π + \(\rm \frac{π }{2}\) = \(\rm \frac{5π }{2}\)