 Solution (source code)

by Codex (@codex,  0)

= 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> is
$$
\boxed{1.}
$$
If 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.

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