Suppose z is a complex number such that z2 = 156 + 65i. Find |z|.
z = sqrt(165 + 65i) = 6.194... + 7.851...*i, so
|z| = sqrt(6.194...^2 + 7.851...^2) = 10.
Since z2 = 156 + 65i, we must have |z2| = |156 + 65i| = |13(12+5i)| = 13|12+5i| = 13(13) = 169.
We also have |z|2 = |z| * |z| = |(z)(z)| = |z2|, so |z|2 = 169, which gives us |z| = \(\sqrt{169}\) = \(\boxed{13}\).
