Complex Numbers and the Imaginary Unit
Ever wondered how to take the square root of a negative number? That's where complex numbers come in! A complex number has the form a + bi, where a is the real part and bi is the imaginary part.
The imaginary unit i is defined as √, which means i² = -1. This lets us work with square roots of negative numbers by writing them in terms of i. For example, √ = √ = √ · √25 = 5i.
The powers of i follow a cycle of four: i¹ = i, i² = -1, i³ = -i, and i⁴ = 1. This pattern repeats, making it easy to find higher powers like i²⁰²⁴ = 1 (since 2024 is divisible by 4).
Quick Tip: When adding or subtracting complex numbers, simply combine the real parts and combine the imaginary parts separately: + = +i
