Let $z\in\mathbb{C}$.
What is the correct way of square rooting both sides of the inequality $$\text{Im}(z)^2 < 3\text{Re}(z)^2\;\text{?}$$
Let $z\in\mathbb{C}$.
What is the correct way of square rooting both sides of the inequality $$\text{Im}(z)^2 < 3\text{Re}(z)^2\;\text{?}$$
$$ |\text{Im}\,(z)| < \sqrt3\,|\text{Re}\,(z)|. $$
As in any other such case:
$$\forall\,x,a\in\Bbb R\,\,,\,a>0\;\;\;,\;x^2
So here $$Im(z)^2<3\,Re(z)^2\Longrightarrow |Im(z)|<\sqrt 3\,|Re(z)|$$