Question

which complex number has a distance of √17 from the origin on the complex plane?a. 2 15ib. 17 ic. 20 - 3id. 4 - i

Answer 1

Let $z=a+bi$. $|z| = \sqrt{a^2+b^2}$, so:
$|z_a| = \sqrt{0+15^2} = 15 \neq \sqrt{17} \\ |z_b| = \sqrt{0+17^2} = 17\neq \sqrt{17} \\ |z_c| = \sqrt{20^2+3^2} \ \textgreater \ \sqrt{20^2} = 20\ \textgreater \ \sqrt{17} \\\\ \boxed{|z_d| = \sqrt{4^2+1^2} = \sqrt{16+1} = \sqrt{17}}$