Let ‘z’ and ‘w’ be two complex numbers such that $\left|z\right|\le 1,\left|w\right|\le 1and|z+i\overline{w}|=|z-iw|=2$  then which of the following is incorrect? 

Because $\left|z\right|\le 1and\left|iw\right|\le 1and|z-iw|=2,$ so ‘z’, iw are end points of diameter of $x^2+y^2=1.$
Similarly ‘z’ and $\overline{iw}$  are also end points of same diameter (because $(z-\overline{iw})=2$)

$\Rightarrow iw=\overline{iw}\Rightarrow iw$ lies on real axis 
$\Rightarrow$ z lies on real axis  
$\Rightarrow eitherz=1,iw=-1orz=-1,iw=1$