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\, √(2)\mleft(\cos \mleft((5\pi)/(4)\mright)+i\sin \mleft((5\pi)/(4)\mright)\mright)`

Therefore the correct answer is the letter D.