Math
Complex numbers.
Definition
Complex numbers are numbers in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit defined as √(-1). They extend the real number system so that every polynomial equation has a solution.
Examples
Real-world.
- 1 3 + 2i and 3 - 2i are complex conjugates
- 2 The solutions to x² + 1 = 0 are x = i and x = -i
- 3 Electrical engineers use complex numbers to analyze AC circuits
Key Fact
i = √(-1); i² = -1; i³ = -i; i⁴ = 1