Let z_1=1+2 i, z_2=2+i, 1/z_1+1/z_2=6/w, and z=(i w)/(2-w̄). Consider the statements ( S_1)|z|=5/(√ 17) ( S_2) (z)+ (w)= tan^-1(5/3). Then

Let $\displaystyle z_1=1+2 i, z_2=2+i, \frac{1}{z_1}+\frac{1}{z_2}=\frac{6}{w}$, and $\displaystyle z=\frac{i w}{2-\bar{w}}$.Consider the statements $\displaystyle \left(\mathrm{S}_1\right)|z|=\frac{5}{\sqrt{17}}$ $\displaystyle \left(\mathrm{S}_2\right) \quad \arg (z)+\arg (w)=\tan ^{-1}\left(\frac{5}{3}\right)$. Then