Rectangular and polar forms of complex numbers

The  exercise appears under the Precalculus Math Mission. This exercise continues to understand the connection between the rectangular and polar forms of a complex number.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the coordinates and plot the point: This problem provides a complex number in polar form. The student is expected to find the coordinate of the point in a rectangular form and plot the appropriate point on the complex plane.Rapfocn1.png
 * 2) Select the true statements: This problem provides a complex number sketched on a complex plane. The student is expected to select the true statements from a collection of possible statements below the grid.Rapfocn2.png

Strategies
Knowledge of the polar form of a complex number is encouraged to ensure success on this exercise.
 * 1) This problem requires a student to find the appropriate radius and angle to make a complex number.
 * 2) The radius is the magnitude of the complex number and the angle is the arctan(y/x).
 * 3) The rectangular coordinates of a complex number are rcos(theta) and rsin(theta) from it's polar form.
 * 4) Answers are to be rounded to the tenths place, one decimal place of accuracy.
 * 5) This problem should always be performed correctly because the answer does not need to be submitted until it is moved to the correct place.
 * 6) At least one statement will be true on the multiple select problem.

Real-life Applications

 * 1) Imaginary numbers are used in chaos theory for predicting chaotic situations, like earthquakes and stock markets.
 * 2) Imaginary numbers can be used to model geometry on the Cartesian plane.
 * 3) The complex plane representation of complex numbers can be used to better understand polar coordinates.