Imaginary number

Definition

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit $i$, where $i = \sqrt{-1}$. Imaginary numbers are used to extend the real numbers to complex numbers.

5 Must Know Facts For Your Next Test

1. The imaginary unit $i$ satisfies $i^2 = -1$.
2. Imaginary numbers can be added, subtracted, multiplied, and divided similar to real numbers, but with special rules for $i$.
3. A complex number is composed of a real part and an imaginary part (e.g., $a + bi$).
4. In algebraic equations, imaginary numbers often appear when solving equations with negative square roots.
5. When graphed, imaginary numbers are placed on the vertical axis of the complex plane.

Review Questions

• What is the value of $i^2$?
• How do you represent the square root of a negative number using an imaginary unit?
• What does a complex number look like in standard form?

Related terms

Complex Number: A number in the form $a + bi$, where $a$ and $b$ are real numbers and $i = \sqrt{-1}$.

Real Number: A value representing a quantity along a continuous line without an imaginary component.

Complex Plane: A two-dimensional plane where each point represents a complex number; the horizontal axis represents the real part and the vertical axis represents the imaginary part.