Question

DeMoivre’s Theorem

[6( cos 70° + i sin 70°)]³

Answer 1

`[6(\cos 70^(\circ) + i \sin 70^(\circ))]^3\\\\=6^3[ \cos ( 3 * 70)^(\circ) + i \sin ( 3 * 70)^(\circ)]\\\\=216 [\cos(210^(\circ)) + i \sin( 210^(\circ))]\\\\=216[\cos(2* 90^(\circ) + 30^(\circ)) + i \sin( 2 * 90^(\circ) + 30^(\circ))]\\\\=216[-\cos 30^(\circ)-i\sin 30^(\circ)]\\\\=216\left[-\frac{ \sqrt 3} 2 - i \cdot \frac 12 \right]\\\\=-108\left(\sqrt 3 +i \right)`