# Complex Numbers

## Vocabulary

### complex conjugate

for a given complex number $a+bi$, the number with the same real part and the opposite imaginary part, or $a-bi$

### complex number

sum of a real number and a pure imaginary number

### complex plane

plane used to locate points that represent complex numbers in terms of distance from the real axis and the imaginary axis

### discriminant

$b^2-4ac$

### imaginary axis

vertical axis in the complex plane, representing the set of pure imaginary numbers

### imaginary number

number of the form $bi$, where $b$ is a real number and $i$ is the imaginary unit

### imaginary unit

square root of -1, written as $i$:
$i=\sqrt{-1}$

### like terms

terms that contain the same variable (or variables) with the same exponents

### perfect square trinomial

trinomial of the form $a^2+2ab+b^2$ or $a^2-2ab+b^2$ that can be written as the square of a binomial

equation, where $a$, $b$, and $c$ are real numbers and $a\neq0$, expressed as:
$ax^2 + bx + c = 0$

formula used to solve a quadratic equation of the form $ax^2+bx+c=0$ by using its coefficients:
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

expression that contains at least one radical sign, $\sqrt{\phantom{0}}$

### real axis

horizontal axis in the complex plane, representing the set of real numbers

### real number

number in the set of all rational and irrational numbers

### real root

solution of an equation that is also a real number

### standard form of a complex number

form for any real numbers $a$ and $b$ written as:
$a+bi$

### term

part of an expression that is separated from other parts by addition or subtraction