Operations with Complex Numbers

Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

Simplify:1. 2x + 3y – x + y

= x + 4y

2. (x + 3)(x – 3)

= x2 – 3x + 3x - 9

= x2 – 9

3.

( )

4. i2

Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

Adding complex numbers

Find the sum of 4 + 2i and 2 – 5i.

Keep the real numbers together,

keep the imaginary numbers together.

is similar toadding polynomials.

Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

4 + 2i + 2 - 5i 6 - 3i

Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

Subtracting complex numbers

+− −( )

subtracting polynomials.

is similar to

Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

Multiplying complex numbers is similar

to multiplying polynomials.

Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

The complex conjugate

is similar to

the radical conjugate.

( )

Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

Dividing complex numbers

is similar to

we just divided complex numbers.