Find complex numbers according to absolute value and angle

The  exercise appears under the Algebra II Math Mission and Precalculus Math Mission. This exercise introduces the concept of the absolute value, or magnitude, for complex numbers.

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


 * 1) Express $$z_1$$ in rectangular form, as $$z_1=a+bi$$.: This problem mentions the magnitude and students are expected to express $$z_1$$ in rectangular form, as $$z_1=a+bi$$. Find complex numbers according to absolute value and angle.PNG

Strategies
Knowledge of the Pythagorean theorem and radical simplification are encouraged to ensure success on this exercise.
 * 1) A complex number of the form $$z_1=a+bi$$ has:
 * 2) A magnitude of $$|z|=\sqrt{a^2+b^2}$$.
 * 3) An angle of $$\theta=\text{arctan}(\frac{b}{a})$$

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.