Imaginary and complex numbers

This lesson we learn:
- Imaginary numbers: Their squares are negative!
- Working with imaginaries: Add, subtract, multiply, and divide imaginary numbers
- Complex numbers: Combining the real and the imaginary
- The complex plane: A way to graph complex numbers
- Powers of i: Raising i to positive and negative integer powers

There is no real number that squared results in a negative number, the resolution of this issue by defining the imaginary unit “i” as the square root of -1.
The square root of any negative real number can be written in terms of the imaginary unit or often called imaginary numbers.

When an imaginary number involves a radical, place “i” in front of the radical.
Complex numbers is any number that can be written as a + bi.
To divide complex numbers, we apply the technique used to rationalize the denominator with multiply the numerator and denominator (dividend and divisor) by the conjugate of the denominator and the result can then be resolved into standard form, a+bi.
The distributive property also applies for multiplying complex numbers by use the fact that i^2=−1 to resolve the result into standard form: a+bi.
The result of adding, subtracting, multiplying, and dividing complex numbers is a complex number.
Use complex numbers to describe solutions to quadratic equations that are not real
Adding and subtracting complex numbers is similar to adding and subtracting like terms, we add or subtract the real parts and then the imaginary parts.

Imaginary numbers - Working with imaginaries | Algebra II: 

Complex numbers - The complex plane | Algebra II: 

Powers of i | Complex numbers - Algebra II: