Complex Numbers and the Complex Plane page 22

Square Roots of Negative Numbers: The square root of any negative number can be written as a multiple of $i$ .
Plotting Complex Numbers: To plot a complex number, two number lines are crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis.
Addition and Subtraction: Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts.
Multiplication and Division: Complex numbers can be multiplied and divided.
Procedure for Multiplication: To multiply complex numbers, distribute just as with polynomials.
Procedure for Division: To divide complex numbers, multiply both the numerator and denominator by the complex conjugate of the denominator to eliminate the complex number from the denominator.
Cyclic Nature of Powers: The powers of $i$ are cyclic, repeating every fourth one.

Complex Conjugate: The complex number in which the sign of the imaginary part is changed and the real part of the number is left unchanged; when added to or multiplied by the original complex number, the result is a real number.
Complex Number: The sum of a real number and an imaginary number, written in the standard form $a + bi$ , where $a$ is the real part, and $bi$ is the imaginary part.
Complex Plane: A coordinate system in which the horizontal axis is used to represent the real part of a complex number and the vertical axis is used to represent the imaginary part of a complex number.
Imaginary Number: A number in the form $bi$ where $i = \sqrt{-1}$ .