Are there always 2 solutions to the square root of a complex number?

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If you have an equation such as $x^2=9$, $x$ will have 2 solutions. But then if you have the equation $x=\sqrt9$, then $x$ cannot be plus minus $3$.

However, does this still follow through with complex numbers? For example, if I was given that

  1. $(x+iy)^2=1-i\quad$ as well as
  2. $x+iy=\sqrt{1-i},$

Would only the first equation have 2 possible values for $x$ and $y$, or would both 1. and 2. have 2 possible solutions?