Add and Subtract Complex Numbers
Learning Outcomes
- Add complex numbers
- Subtract complex numbers
To simplify this expression, you combine the like terms, and . These are like terms because they have the same variable with the same exponents. Similarly, 8 and 2 are like terms because they are both constants, with no variables.
In the same way, you can simplify expressions with radicals.
You can add to because the two terms have the same radical, , just as x and x have the same variable and exponent. The number i looks like a variable, but remember that it is equal to . The great thing is you have no new rules to worry about—whether you treat it as a variable or a radical, the exact same rules apply to adding and subtracting complex numbers. You combine the imaginary parts (the terms with i), and you combine the real parts.
Example
Add.Answer: Rearrange the sums to put like terms together.
Combine like terms.
and
The answer is .
Example
Subtract.Answer: Be sure to distribute the subtraction sign to all terms in the set of parentheses that follows.
Rearrange the terms to put like terms together.
Combine like terms.
and
The answer is .