Question

Use De Moivre's Theorem to write the complex number in standard form.

(see below)

Answer 1

\[[\sqrt2[\cos 10^0 + isin 10^0]]^6 =(\sqrt2)^6[\cos (6\times10^0) + isin ( 6 \times 10^0)]\]
\[=8\cos (60^0) +8 isin ( 6 0^0 ) =8 \times \frac{1}{2} +8 \times i \times \frac{\sqrt3}{2}\]
\[=4 +4 i \sqrt3\]

Answer 2

wow thank you so much! :D