Past exam of the mathematical methods I course of the University of Oxford / 2017 / 1 / a / Solution

Since $(1+i{)}^2=2i$, the two square roots are $1+i$ and $-1-i$. The principal square root is $1+i$, whose real part isIf the notation is meant to include both square-root values, their real parts are $+1$ and $-1$. Stating the principal-branch convention removes that ambiguity.