Dividing complex numbers

The  exercise appears under the Algebra II Math Mission. This exercise introduces and develops the arithmetic of complex numbers.

Types of Problems
There is one type of problem in this exercise:


 * 1) Divide the complex numbers: This problem has two complex numbers that are supposed to be divided. The student is expected to find the correct product and write it in the space provided.Dcn1.png

Strategies
Knowledge of numerical operations and polynomial operations are encouraged to ensure success on this exercise.
 * 1) The quotient of complex numbers are performed by using rationalizing the denominator by multiplying by the conjugate and then replacing i^2 with the value of -1.
 * 2) The conjugate of $$a+bi$$ is $$a-bi$$.
 * 3) The answer should be simplified completely to earn credit.

Real-life Applications

 * 1) Complex numbers have applications as models in non-Euclidean geometries.
 * 2) Complex numbers are used to create fractal images.
 * 3) Complex numbers are a natural extension of the real numbers.