Chapter 8 - Polar Coordinates; Vectors - Section 8.3 The Complex Plane; De Moivre's Theorem - 8.3 Assess Your Understanding - Page 615: 41

$-32+32\sqrt {3}i$

Applying De Moivre's theorem, we have \begin{align*} [4(\cos 40^{\circ}+i\sin 40^{\circ})]^{3}&=4^{3}[\cos(3\cdot40^{\circ})+i\sin(3\cdot40^{\circ})]\\ &=64\left(\cos 120^{\circ}+i\sin120^{\circ}\right)\\ &=64\left(-\frac{1}{2}+\frac{\sqrt {3}}{2}i\right)\\ &= -32+32\sqrt {3}i\end{align*}