Question

Complete the polar form of z.Imaginary axis10181614142iReal axis10-10 -8-6-4-202.46 800-21-41-61N-81-101Write your answers as decimals rounded to the nearest tenth. Express the argument o indegrees, with 0° so < 360°.(cos O + isinSubmit

Answer 1

`(√(16+(-6i)^2),\tan^(-1)(-(3i)/(2)))`

Explanation:

To convert from Cartesian coordinates to polar coordinates:

`\begin{gathered} r=√(x^2+y^2) \\ \theta=\tan^(-1)((y)/(x)) \\ \text{ Polar coordinates would be:} \\ (r,\theta) \end{gathered}`

Therefore, for the given coordinate:

`z(4,\text{ -6i\rparen}`
`\begin{gathered} r=√(4^2+(-6i)^2) \\ \theta=\tan^(-1)(-(3i)/(2)) \end{gathered}`

Hence, the polar coordinates of the given cartesian coordinates:

`(√(16+(-6i)^2),\tan^(-1)(-(3i)/(2)))`