## Key Concepts

• The square root of any negative number can be written as a multiple of i.
• To plot a complex number, we use two number lines, crossed to form the complex plane. The horizontal axis is the real axis, and the vertical axis is the imaginary axis.
• Complex numbers can be added and subtracted by combining the real parts and combining the imaginary parts.
• Complex numbers can be multiplied and divided.
• To multiply complex numbers, distribute just as with polynomials.
• 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.
• The powers of i are cyclic, repeating every fourth one.

## Glossary

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 abi, 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 $i=\sqrt{-1}\\$