Complex num. summary, Cheat Sheet of Mathematics

Complex numbers are written in the form , where

𝑥+𝑖𝑦 𝑥, 𝑦 ∈ ℝ

Imaginary numbers are written in the form , where 𝑦𝑖 𝑦 ∈ ℝ

When complex numbers are written as shown, this is in Cartesian form.

If , there are two distinct real roots

𝑏² − 4𝑎𝑐＞0

If , there is one repeated real root 𝑏² − 4𝑎𝑐=0

If , there are no real roots

𝑏² − 4𝑎𝑐＜0

We can find solutions to a quadratic equation using our calculator for all cases

So, we can find solutions to the equation by extending the number system to include

−1

If a quadratic equation has no real roots and has only real coefficients,

it has two distinct complex roots:

𝑧=𝑥+𝑖𝑦