12. Complex Numbers & Polar Equations

12.01 Complex numbers

12.02 Complex conjugates and moduli of complex numbers

12.03 Graphing complex numbers

12.04 Distance between and midpoints of complex numbers

12.05 Polar form

12.06 Graphing polar equations

12.07 Converting between polar and rectangular equations

United States of America

Grades 9-12

12.06 Graphing polar equations

Interactive practice questions

Consider the point $\left(8,\frac{11\pi}{6}\right)$(8,11π6), in polar coordinates.

a

This point is $\editable{}$ units away from the pole on a polar grid.

b

What is the size of the angle that the point makes with the polar axis? Give your answer in radians.

c

Which of the following shows the location of $\left(8,\frac{11\pi}{6}\right)$(8,11π6) on a polar grid?

A polar coordinate grid with several blue points labeled from A to H. The grid has concentric circles increasing in radius at consistent intervals which represents the axes of the polar coordinate grid. The fifth circle is labeled $10$10 indicating that it is the $10$ th axis. Point $A$A is at $\left(8,\frac{\pi}{3}\right)$(8,π3); point $B$B is at $\left(8,\frac{\pi}{6}\right)$(8,π6); point $C$C is at $\left(8,\frac{11\pi}{6}\right)$(8,11π6); point $D$D is at $\left(8,\frac{5\pi}{3}\right)$(8,5π3); point $E$E is at $\left(4,\frac{\pi}{3}\right)$(4,π3); point $F$F is at $\left(4,\frac{\pi}{6}\right)$(4,π6); point $G$G is at $\left(4,\frac{11\pi}{6}\right)$(4,11π6); point $H$H is at $\left(4,\frac{5\pi}{3}\right)$(4,5π3). The coordinates of all points are not explicitly given in the image and should never be given as answer to any questions/prompts.

Easy

1min

Consider the point $\left(8,\left(-30\right)^\circ\right)$(8,(−30)°), in polar coordinates.

Easy

< 1min

Consider the points that have been graphed on the polar grid below.

Easy

8min

Convert the point $\left(8,9\right)$(8,9) from rectangular coordinates to polar coordinates $\left(r,\theta\right)$(r,θ), where $0^\circ\le\theta<360^\circ$0°≤θ<360°. Give each value correct to two decimal places.

Easy

2min

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