Question

Sa se determine numarul complex al carui patrat este egal cu : 1-i/1+i

Answer 1

$z^{2} = \frac{1-i}{1+i} \Rightarrow z^{2} = \frac{(1-i)^{2} }{(1-i)(1+i)} \Rightarrow z^{2} = \frac{(1-i)^{2}}{2} \Rightarrow z = \frac{\pm(1-i)}{ \sqrt{2} } \Rightarrow \\ \Rightarrow z = \frac{\pm \sqrt{2}\cdot(1-i) }{2}$