Two complex numbers for which the real parts are equal and the imaginary parts are additive inverses. a + bi and a – bi are complex conjugates.

A number in the form a + bi, where a and b are real numbers and i is the square root of −1.

One binomial in a conjugate pair. Given the binomial a + b, the conjugate is a – b; given a – b, the conjugate is a + b.

A pair of binomials that, when multiplied, follow the pattern:

The product of a pair of binomials that are conjugates is the difference of two squares.

The number which, when multiplied together three times yields the original number. For example, the cube root of 64 is 4 because 4 • 4 • 4 = 64.

In the Quadratic Formula, the expression underneath the radical symbol: b² – 4ac. The discriminant can be used to determine the number and type of solutions the formula will reveal.

A number in the form bi, where b is a real number and i is the square root of −1.

The imaginary term, bi, in a complex number a + bi.

The small positive integer just outside and above the radical symbol that denotes the root. For example, denotes the cube root.

A trinomial that is the product of a binomial times itself, such as a² + 2ab + b² (from (a + b)²), and a² – 2ab + b² (from (a – b)²).

The positive square root of a number, as in . By definition, the radical symbol always means to find the principal root. Note that zero has only one square root, itself (since 0 • 0 = 0).

The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: (ab)^x= a^x • b^x

For any real numbers a and b (b ≠ 0) and any positive integer x:

The symbol, , used to denote the process of taking a root of a quantity.

The real term, a, in a complex number a + bi.

A number that when multiplied by itself gives the original nonnegative number. For example, 6 • 6 = 36 and −6 • −6 = 36 so 6 is the positive square of 36 and −6 is the negative square root of 36.

If x² = a², then x = a or x = −a.

completing the square	A method for solving quadratic equations by rewriting one side of the equation as a squared binomial.
complex conjugate	Two complex numbers for which the real parts are equal and the imaginary parts are additive inverses. a + bi and a – bi are complex conjugates.
complex number	A number in the form a + bi, where a and b are real numbers and i is the square root of −1.
conjugate	One binomial in a conjugate pair. Given the binomial a + b, the conjugate is a – b; given a – b, the conjugate is a + b.
conjugate pair	A pair of binomials that, when multiplied, follow the pattern: The product of a pair of binomials that are conjugates is the difference of two squares.
cube root	The number which, when multiplied together three times yields the original number. For example, the cube root of 64 is 4 because 4 • 4 • 4 = 64.
discriminant	In the Quadratic Formula, the expression underneath the radical symbol: b² – 4ac. The discriminant can be used to determine the number and type of solutions the formula will reveal.
distributive property of multiplication	The product of a sum (or a difference) and a number is the same as the sum (or difference) of the product of each addend (or each number being subtracted) and the number. For example, 3(4 + 2) = 3(4) + 3(2), and 3(4 – 2) = 3(4) – 3(2).
extraneous solution	A solution of the simplified form of an equation that does not satisfy the original equation and must be discarded.
imaginary number	A number in the form bi, where b is a real number and i is the square root of −1.
imaginary part	The imaginary term, bi, in a complex number a + bi.
index	The small positive integer just outside and above the radical symbol that denotes the root. For example, denotes the cube root.
perfect cube	A number whose cube root is an integer.
perfect square trinomial	A trinomial that is the product of a binomial times itself, such as a² + 2ab + b² (from (a + b)²), and a² – 2ab + b² (from (a – b)²).
principal root	The positive square root of a number, as in . By definition, the radical symbol always means to find the principal root. Note that zero has only one square root, itself (since 0 • 0 = 0).
product raised to a power rule	The product of two or more non-zero numbers raised to a power equals the product of each number raised to the same power: (ab)^x= a^x • b^x
quotient raised to a power rule	For any real numbers a and b (b ≠ 0) and any positive integer x: For any real numbers a and b (b ≠ 0) and any positive integer x:
radical equation	An equation that contains a radical expression.
radical expression	An expression that contains a radical.
radical symbol	The symbol, , used to denote the process of taking a root of a quantity.
radicand	The number or value under the radical symbol.
rational exponent	An exponent that is a fraction.
rationalizing a denominator	The process by which a fraction containing radicals in the denominator is rewritten to have only rational numbers in the denominator.
real part	The real term, a, in a complex number a + bi.
square root	A number that when multiplied by itself gives the original nonnegative number. For example, 6 • 6 = 36 and −6 • −6 = 36 so 6 is the positive square of 36 and −6 is the negative square root of 36.
square root property	If x² = a², then x = a or x = −a.