Distance and midpoint on the complex plane

The  exercise appears under the Precalculus Math Mission. This exercise introduces the distance and midpoint formulas as applied to complex numbers.

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


 * 1) Find the distance and the midpoint: This problem provides two complex numbers and a grid. The student is expected to find the distanced between the complex numbers and the midpoint, and write them in the space provided.Damotcp1.png
 * 2) Find the distance and plot the points: This problem provides two complex numbers and describes some operations. The student is expected to find the distance between the points, answer some questions, and plot some points on a provided coordinate axis.Damotcp2.png

Strategies
Knowledge of the distance and midpoint formulas are encouraged to ensure success on this exercise.
 * 1) The distance formula is essentially the Pythagorean theorem applied to the distances between the x and y coordinates.
 * 2) The distance is to be rounded to the tenths place, one decimal place.
 * 3) The midpoint is the average of the x's and the y's.
 * 4) The midpoint is located directly in between the two complex numbers.

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.