I was working on Complex variable topics, curve parameterization on the complex plane, and I came across Parametrizing shapes, curves, lines in $\mathbb{C}$ plane since I'm struggling a bit and I'm having some problems.
The thing is if we have the circle described by $(x-1)^2 + y^2 = 1$, and we decide to set $y=10$, the value that $x$ should take is $1 +i\sqrt{99}$, but how should this be interpreted? With a second imaginary axis that takes the value of $\sqrt{99}$? Adding $\sqrt{99}$ to the term of the existing imaginary value (this is, $y$)?