1.3 Complex Numbers

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Complex Number = a + bi a is the Real part

b is the Imaginary part

If b = 0, then a + bi = a

If a = 0, and b does not equal 0, the Complex Number is a Pure Imaginary Number, eg. 3i

If a does not equal 0 and b does not equal 0, it is a Non-real Complex Number, eg. 1 + 6i

A Complex Number written in the form a + bi or a + ib

Important Words

Complex Number

Real Part

Imaginary Part

Pure Imaginary Number

Nonreal Complex Number

Standard Form

Complex Conjugate

What is i?

i is an Imaginary Number

It represents the square root of -1

i squared = -1

Using i in operations Use square root of -a = i(square root of a) before anything else

Add or subtract Real Parts and add or subtract Imaginary Parts

FOIL when multiplying

(a + bi)(a - bi) are Complex Conjugates.

To divide 2 Complex Numbers multiply both the numerator and the denominator by the complex conjugate of the denominator