Question

Find the trigonometric form of the complex number. Hint: Graph the complex number first to give yourself a visual representation.

Answer 1

First, let's graph the complex number:

The trigonometric form will be given by:

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

The angle θ here is 225° (5π/4), the r-value will be

$\begin{gathered} r=\sqrt[]{(-2)^2+(-2)^2} \\ \\ r=\sqrt[]{4+4} \\ \\ r=\sqrt[]{8}=2\, \sqrt[]{2} \end{gathered}$

Now we have the trigonometric representation:

$-2-2i=2\, \sqrt{2}\mleft(\cos \mleft(\frac{5\pi}{4}\mright)+i\sin \mleft(\frac{5\pi}{4}\mright)\mright)$

Therefore the correct answer is the letter D.