Question

Write the following complex number in trigonometric form. Write the magnitude in exact form. Write the argument in radians and round it to twodecimal places if necessary.-2 - 8i

Answer 1

Answer:

$2\sqrt{17}(cos\text{ 4.47}+isin4.47)$

Step-by-step explanation:

The trigonometric form of a complex number is represented by the following equation:

$\begin{gathered} z=r(cos\theta+isin\theta) \\ where, \\ r=\text{ the hypotenuse } \\ \theta=\text{ the angle } \end{gathered}$

For the given complex number:

Find the hypotenuse and angle:

$\begin{gathered} tan\theta=\frac{8}{2} \\ \theta=\tan^{-1}(4) \\ \theta=75.96 \\ \theta=76\text{ degrees} \\ \\ r=\sqrt{(-8)^2+(-2)^2} \\ r=2\sqrt{17} \end{gathered}$

Hence, writing the complex number in trigonometric form:

$2\sqrt{17}(cos\text{ 4.47}+isin4.47)$