 # Complex Numbers.

## Presentation on theme: "Complex Numbers."— Presentation transcript:

Complex Numbers

Definition of pure imaginary numbers:
Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.

it is a symbol for a specific number
Definition of pure imaginary numbers: i is not a variable it is a symbol for a specific number

Simplify each expression.

Simplify each expression.
Remember Remember

Definition of Complex Numbers
Any number in form a+bi, where a and b are real numbers and i is imaginary unit.

Definition of Equal Complex Numbers
Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d

When adding or subtracting complex numbers, combine like terms.

Solving quadratic functions with complex numbers.
subtract 2 Take the square root of both sides simplify

Simplify.

Simplify.

Multiplying complex numbers.
To multiply complex numbers, you use the same procedure as multiplying polynomials.

Simplify. F O I L

Simplify. F O I L

CONJUGATES Each imaginary unit has a conjugate. Two imaginary units are conjugates if and only if their products are a real number.

Dividing complex numbers.
To divide complex numbers you must multiply the numerator and denominator by the conjugate of the denominator.

What’s the conjugate of the denominator?

Your turn. Write in standard form by dividing.

Graphing complex numbers
y-axis is the imaginary axis. x-axis is the real numbers Identify the numbers plotted.