Algebra 2 · Unit 2 · Topic 2.2
The Imaginary Unit and Complex Numbers
A complex number has form a + bi, where a and b are real and i² = −1.
Definition and explanation
A complex number has form a + bi, where a and b are real and i² = −1. The real part is a and the imaginary part is b; real numbers are included when b = 0.
Worked example
Solve x² + 49 = 0 in the complex numbers. Since x² = −49 and (7i)² = −49, the solutions are x = 7i and x = −7i. There are no real solutions.
Common mistake
The imaginary unit is not −1: its square, rather than i itself, equals −1.
Key takeaway
A complex number has form a + bi, where a and b are real and i² = −1.
Explain each step of the worked example, then check the units, signs, and conditions that apply.
Further reading
Topic coverage was checked against the openly available OpenStax Intermediate Algebra 2e, Algebra and Trigonometry 2e, and Introductory Statistics 2e textbooks. The explanations and examples on this site are independently written; textbook prose, exercises, and artwork are not reproduced.