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

`2√(17)(cos\text{ 4.47}+isin4.47)`

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=(8)/(2) \\ \theta=\tan^(-1)(4) \\ \theta=75.96 \\ \theta=76\text{ degrees} \\ \\ r=√((-8)^2+(-2)^2) \\ r=2√(17) \end{gathered}`

Hence, writing the complex number in trigonometric form:

`2√(17)(cos\text{ 4.47}+isin4.47)`