## Trigonometry (11th Edition) Clone

$z$ and $iz$ have the same absolute value. $z$ and $iz$ are perpendicular to each other with the same absolute value.
Let $z = a + bi$ The absolute value of $z$ is $\sqrt{a^2 + b^2}$ Now, $iz = i(a + bi) = bi^2 + ai = -b + ai$ (since $i^2 = -1$) The absolute value of $iz$ is $\sqrt{(-b)^2 + a^2}$ = $\sqrt{a^2 + b^2}$ Therefore, $z$ and $iz$ have the same absolute value. $z$ and $iz$ are perpendicular to each other with the same absolute value.