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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) = 2? then find arg(z2)
Concept:Properties of complex numbersz = \(\rm \overline{z}\), if z is purely realz = - \(\rm \overline{z}\), if z is either 0 or purely imaginaryarg(zn?) = n arg(z)Calculation:Given that\(\rm \overline{z_{1}} - i \overline{z_{2}^{2}}\) = 0z1 = -i z22arg(z1) - arg(z2) = 2?arg(-i z22) - arg(z2) = 2?arg(-i) + arg(z22) - arg(z2) = 2?\(\rm \frac{-?}{2} \)+ 2 arg(z2) - arg(z2) = 2?arg(z2) = 2? + \(\rm \frac{? }{2}\) = \(\rm \frac{5? }{2}\)
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