Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set - Page 787: 15

$z=-2i, 2i, -3, 3$

$z^4-5z^2-36=0$ $x=z^2$ $z^4-5z^2-36=0$ $x^2-5x-36=0$ $(x+4)(x-9)=0$ $(z^2+4)(z^2-9)=0$ $(z^2+4)(z-3)(z+3)=0$ $z-3=0$ $z=3$ $z+3=0$ $z=-3$ $z^2+4=0$ $z^2=-4$ $\sqrt {z^2}=\sqrt {-4}$ $z=\sqrt{4*-1}$ $z=±2i$