If k > 0, |z| = |w| = k and α=z−wk2+zw, then Re(α) equals

α=z−wk2+zw⇒α=z−wk2+zwBut zz=ww=k2. Hence⇒ α¯=k2z−k2w¯k2+k2zk2w¯=w¯−zzw¯+k2=−α⇒ α+α¯=0⇒ Re⁡(α)=0

If k > 0, |z| = |w| = k and α=z−wk2+zw, then Re(α) equals

α=z−wk2+zw⇒α=z−wk2+zwBut zz=ww=k2. Hence⇒ α¯=k2z−k2w¯k2+k2zk2w¯=w¯−zzw¯+k2=−α⇒ α+α¯=0⇒ Re⁡(α)=0

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If k > 0, |z| = |w| = k and $α = \frac{z - w}{k^{2} + z w}$ , then Re( $α$ ) equals

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$α = \frac{z - w}{k^{2} + z w} \Rightarrow α = \frac{z - w}{k^{2} + z w}$

But $z z = w w = k^{2}$ . Hence

$\Rightarrow \bar{α} = \frac{\frac{k^{2}}{z} - \frac{k^{2}}{\bar{w}}}{k^{2} + \frac{k^{2}}{z} \frac{k^{2}}{\bar{w}}} = \frac{\bar{w} - z}{z \bar{w} + k^{2}} = - α$

$\begin{array}{ll} \Rightarrow α + \bar{α} = 0 \\ \Rightarrow Re (α) = 0 \end{array}$

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If k > 0, |z| = |w| = k and $α = \frac{z - w}{k^{2} + z w}$ , then Re( $α$ ) equals