$$\sqrt { p } + \sqrt { q } = 1$$
$p=\left(-\sqrt{q}+1\right)^{2}$
$q\geq 0\text{ and }-\sqrt{q}+1\geq 0$
$q=\left(-\sqrt{p}+1\right)^{2}$
$p\geq 0\text{ and }-\sqrt{p}+1\geq 0$
$p=\left(-\sqrt{q}+1\right)^{2}$
$q=1\text{ or }arg(-\sqrt{q}+1)<\pi $
$q=\left(-\sqrt{p}+1\right)^{2}$
$p=1\text{ or }arg(-\sqrt{p}+1)<\pi $
