Add and Subtract Complex Numbers

Adding and Subtracting Complex Numbers

Complex numbers are written in the form (a+bi), where (a) is the real part and (b) is the coefficient of (i). To add or subtract them, combine like parts: real with real, and imaginary with imaginary.

1) Line up the parts

Rewrite each number in standard form if needed. Make sure the real parts and the imaginary parts are easy to identify.

2) Combine like terms

• Add or subtract the real parts.
• Add or subtract the coefficients of (i).

For example, if you see ((3+2i) + (5-7i)), combine real parts (3+5) and imaginary parts (2i + (-7i)).

3) Simplify fully

Write the result in the form (a+bi). If the imaginary part becomes zero, the answer is just a real number. If the real part becomes zero, the answer is just an imaginary number such as (bi).

Check your work

A good check is to group the real and imaginary parts separately and verify that no (i^2) terms appear. In basic addition and subtraction of complex numbers, you should only be combining matching parts, not multiplying.

Common mistake

Do not combine the real and imaginary parts together. For example, (4+3i) is not (7i); it has two separate parts that must be handled separately.