Use de Moivre’s Formula to calculate (2 + 2i)^3.

Question

Use de Moivre’s Formula to calculate [latex](2 + 2i)^3[/latex].

Accepted Answer

[latex](2 + 2i)^3 = \left[2 \sqrt{2} \left(\cos (\frac{\pi }{4} ) + \sin (\frac{\pi }{4} )\right) \right] ^3[/latex]

[latex]= (2 \sqrt{2})^3 \left(\cos (\frac{3 \pi }{4} ) + i \sin (\frac{3 \pi }{4} )\right)[/latex]

[latex]= 16 \sqrt{2} \left(- \frac{1}{\sqrt{2} } + i \frac{1}{\sqrt{2} } \right)[/latex]

[latex]= -16 + 16 i[/latex]

Question 9.1.12: Use de Moivre’s Formula to calculate (2 + 2i)^3.