Classify complex numbers

The  exercise appears under the Algebra II Math Mission. This exercise practices classifying complex numbers.

Types of Problems
There is one type of problem in this exercise:
 * 1) What type of number is __?: This problem has a number, and the student is asked to find which type of number it is. There are 3 choices: whole real, pure imaginary, or complex. There may be more than one answer.

Strategies
Basic knowledge of classifying complex numbers is needed to ensure success while doing this exercise.
 * 1) A complex number $$z=a+bi$$ has only two types of components: real (a</math) and imaginary $$b$$. Using this, students can classify $$z$$ as either:
 * 2) Real, if $$b=0$$,
 * 3) Pure imaginary, if $$a=0$$, or
 * 4) Complex, for all real values of $$a$$ and $$b$$

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.