# Key Concepts & Glossary

## 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
*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 [latex]i=\sqrt{-1}\\[/latex]

## Licenses & Attributions

### CC licensed content, Shared previously

- Precalculus.
**Provided by:**OpenStax**Authored by:**Jay Abramson, et al..**Located at:**https://openstax.org/books/precalculus/pages/1-introduction-to-functions.**License:**CC BY: Attribution.**License terms:**Download For Free at : http://cnx.org/contents/[email protected]..