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Question: If k \> 0, \| z \| = \| w \| = k, and a = \(\frac{z - \bar{\omega}}{k^{2} + \bar{z}\bar{\omega}}\) t...

If k > 0, | z | = | w | = k, and a = z−ωˉk2+zˉωˉ\frac{z - \bar{\omega}}{k^{2} + \bar{z}\bar{\omega}} then Re (a) equals

A

k2\frac{k}{2}

B

k

C

0

D

None of these

Answer

0

Explanation

Solution

Sol. αˉ\bar{\alpha}= zˉ−ωK2+zˉω\frac{\bar{z} - \omega}{K^{2} + \bar{z}\omega}

zzˉ=ωωˉ=K2z\bar{z} = \omega\bar{\omega} = K^{2}

αˉ\bar{\alpha} = ωˉ−zzωˉ+k2\frac{\bar{\omega} - z}{z\bar{\omega} + k^{2}}= – a

αˉ\bar{\alpha}+a = 0, Re(a) = 0