# Adding and Subtracting Complex Numbers

To add or subtract two complex numbers , simply add the real and imaginary parts separately.

Example 1:

Simplify.

$\left(3+5i\right)+\left(-1-i\right)$

By the Commutative and Associative Properties,

$\left(3+5i\right)+\left(-1-i\right)=\left(3+\left(-1\right)\right)+\left(5i+\left(-i\right)\right)$

Simplify.

$=2+4i$

The sum is $2+4i$ .

Example 2:

Simplify.

$\left(3-2i\right)-\left(5-4i\right)$

By the Commutative and Associative Properties,

$\left(3-2i\right)-\left(5-4i\right)=\left(3-5\right)+\left[-2-\left(-4\right)\right]i$

Simplify.

$=-2+2i$

The difference is $-2+2i$ .