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

Answer:

$(\sqrt{16+(-6i)^2},\tan^{-1}(-\frac{3i}{2}))$

Step-by-step explanation:

To convert from Cartesian coordinates to polar coordinates:

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

Therefore, for the given coordinate:

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

Hence, the polar coordinates of the given cartesian coordinates:

$(\sqrt{16+(-6i)^2},\tan^{-1}(-\frac{3i}{2}))$