Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.4 De Moivre's Theorem: Powers and Roots of Complex Numbers - 8.4 Exercises - Page 377: 46

$(cos~\theta+i~sin~\theta)^2 = cos^2~\theta - sin^2~\theta + 2i~cos~\theta ~sin~\theta$

$(cos~\theta+i~sin~\theta)^2 = cos^2~\theta + 2i~cos~\theta ~sin~\theta - sin^2~\theta$ $(cos~\theta+i~sin~\theta)^2 = cos^2~\theta - sin^2~\theta + 2i~cos~\theta ~sin~\theta$