First, let's graph the complex number:
The trigonometric form will be given by:
[tex]-2-2i=r(\cos \theta+i\sin \theta)[/tex]
The angle θ here is 225° (5π/4), the r-value will be
[tex]\begin{gathered} r=\sqrt[]{(-2)^2+(-2)^2} \\ \\ r=\sqrt[]{4+4} \\ \\ r=\sqrt[]{8}=2\, \sqrt[]{2} \end{gathered}[/tex]
Now we have the trigonometric representation:
[tex]-2-2i=2\, \sqrt{2}\mleft(\cos \mleft(\frac{5\pi}{4}\mright)+i\sin \mleft(\frac{5\pi}{4}\mright)\mright)[/tex]
Therefore the correct answer is the letter D.
