Write the complex number in trigonometric form, using degree measure for the argument.
-15 - 20i
A) 25(cos 306.9° + i sin 306.9°)
B) 25(cos 126.9° + i sin 126.9°)
C) 25(cos 233.1° + i sin 233.1°)
D) 25(cos 53.1° + i sin 53.1°)

Question

Quizplus · Accepted Answer

The complex number $15 - 20i$ can be written in trigonometric form as $r(\cos \theta + i\sin \theta)$, where $r = \sqrt{15^2 + (-20)^2} = 25$ and $\theta = \tan^{-1}\left(\frac{-20}{15}\right)$. Calculating $\theta$ gives an angle in the fourth quadrant, approximately $306.9^\circ$, since $\tan^{-1}$ of a negative number in this context indicates an angle measured clockwise from the positive x-axis.

Write the Complex Number in Trigonometric Form, Using Degree Measure