1. Operations with Complex Numbers
Radicals
Operations with Complex Numbers

2. Remember … 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.

3. Add Complex Numbers Adding complex numbers is similar to
adding polynomials.
Find the sum of 4 + 2i and 2 – 5i.
Keep the real numbers together,
keep the imaginary numbers together.
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

4. Graph
4 + 2i i
6 - 3i
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

5. Subtract Complex Numbers
Subtracting complex numbers
is similar to
subtracting polynomials. − −
( ) +
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

6. Multiply Complex Numbers
Multiplying complex numbers
is similar to
multiplying polynomials.
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

7. The Complex Conjugate The complex conjugate is similar to
the radical conjugate.
( )
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.

8. Divide Complex Numbers
Dividing complex numbers
is similar to
Hey …
we just divided complex numbers.
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.