Complex numbers and equations

Use complex arithmetic to express and check nonreal solutions.

Meaning

Complex numbers have the form where are real and They allow equations requiring square roots of negative numbers.

Example

The complex solutions of are and Since it satisfies the equation. is not a negative real number; its square is -1. The usual ordering of real numbers does not extend to all complex numbers.

Practice for this concept

Scope and references

Topics

The imaginary unit, complex arithmetic, conjugates, nonreal solutions

Learning goal

Use complex arithmetic to express and check nonreal solutions.

Helpful background

Check that real squares cannot be negative and explore the domain of square roots.