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Let z1 and z2 be two complex numbers such that \(\rm \overline{z_{1}} - i \overline{z_{2}^{2}}\) = 0 and arg(z1) - arg(z2) = 2π then find arg(z2)


1. π
2. 5π/4
3. 5​π/2
4. 3​π/2

1 Answer

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Best answer
Correct Answer - Option 3 : 5​π/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 + \(\rm \frac{π }{2}\)\(\rm \frac{5π }{2}\)

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