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