Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2005 / Paper 2 / 5 / a / Solution

The point $1+i$ has modulus $\sqrt{2}$ and argument $\pi /4$ modulo $2\pi$. Taking complex square roots halves the argument and takes the square root of the modulus:The two roots are opposite points in the complex plane, explicitly $\pm [\sqrt{(\sqrt{2}+1)/2}+i\sqrt{(\sqrt{2}-1)/2}]$.