Find the sq. Root of z=1-i

We have, z = 1 - i Now, Re (z) = 1 |z| = \sqrt{{(1)}^{2} + {(- 1)}^{2}} = \sqrt{1 + 1} = \sqrt{2} Now, \sqrt{z} = \pm [\sqrt{\frac{|z| + Re (z)}{2}} - i \sqrt{\frac{|z| - Re (z)}{2}}] \Rightarrow \sqrt{1 - i} = \pm [\sqrt{\frac{\sqrt{2} + 1}{2}} - i \sqrt{\frac{\sqrt{2} - 1}{2}}]