Complex Numbers: Form and Operations

Vocabulary flashcards covering core concepts from Form, Imaginary numbers, and Performing Operations for complex numbers.

Complex numbers

Numbers of the form a + bi, where a and b are real numbers and i^2 = -1.

Imaginary unit i

The unit with i^2 = -1; i is the square root of -1.

Real part

The 'a' in a + bi; the real component of a complex number.

Imaginary part

The 'bi' portion in a + bi; the imaginary component; b is the imaginary coefficient.

Addition and subtraction of complex numbers

Add or subtract by combining real parts together and imaginary parts together.

FOIL method

First-Outer-Inner-Last method used to multiply complex numbers, applying i^2 = -1 to simplify.

i^2 = -1

Rule that replaces i^2 with -1 in products involving i.

Division by a complex number

To divide by a complex number, multiply numerator and denominator by the conjugate of the denominator to rationalize.

Conjugate of a complex number

For a + bi, the conjugate is a - bi; used to rationalize division and eliminate i from the denominator.