# Tricky complex numbers question

by thomas49th
Tags: complex, numbers, tricky
 P: 656 1. The problem statement, all variables and given/known data Harder: given that √(−15 − 8i) = ±(1 − 4i) obtain the two solutions of the equation z² + (−3 + 2i)z + 5 − i = 0 2. Relevant equations I can easily prove √(−15 − 8i) = ±(1 − 4i) but that's not important 3. The attempt at a solution I would of thought that a compex solution would be a + b and a - b, but a quick glance at the answers shows 2 completely different complex numbers - no complex conjugates. Well seperating the equation into real and imaginary parts then solving for z: real: (z² - 3z + 5) = 0 => $$z = \frac{3\pm i \sqrt{11}}{2}$$ imag: (2z - 1) = 0 => z = 0.5 This isn't taking me anywhere nice... Ideas!? :) Thanks