Add and Subtract Complex Numbers
Learning Outcomes
- Add complex numbers
- Subtract complex numbers
[latex](6x+8)+(4x+2)[/latex]
To simplify this expression, you combine the like terms, [latex]6x[/latex] and [latex]4x[/latex]. 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.[latex](6x+8)+(4x+2)=10x+10[/latex]
In the same way, you can simplify expressions with radicals.[latex] (6\sqrt{3}+8)+(4\sqrt{3}+2)=10\sqrt{3}+10[/latex]
You can add [latex] 6\sqrt{3}[/latex] to [latex] 4\sqrt{3}[/latex] because the two terms have the same radical, [latex] \sqrt{3}[/latex], just as [latex]6[/latex]x and [latex]4[/latex]x have the same variable and exponent. The number i looks like a variable, but remember that it is equal to [latex]\sqrt{-1}[/latex]. 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. [latex](−3+3i)+(7–2i)[/latex]Answer: Rearrange the sums to put like terms together.
[latex]−3+3i+7–2i=−3+7+3i–2i[/latex]
Combine like terms.[latex]−3+7=4[/latex]
and
[latex]3i–2i=(3–2)i=i[/latex]
The answer is [latex]4+i[/latex].Example
Subtract. [latex](−3+3i)–(7–2i)[/latex]Answer: Be sure to distribute the subtraction sign to all terms in the set of parentheses that follows.
[latex](−3+3i)–(7–2i)=−3+3i–7+2i[/latex]
Rearrange the terms to put like terms together.[latex]−3–7+3i+2i[/latex]
Combine like terms.[latex]−3–7=−10[/latex]
and
[latex]3i+2i=(3+2)i=5i[/latex]
The answer is [latex]-10+5i[/latex].Licenses & Attributions
CC licensed content, Original
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Ex 1: Adding and Subtracting Complex Numbers. Authored by: James Sousa (Mathispower4u.com) for Lumen Learning. License: CC BY: Attribution.
- College Algebra. Provided by: OpenStax Authored by: Abramson, Jay et al.. Located at: https://cnx.org/contents/[email protected]:1/Preface. License: CC BY: Attribution. License terms: Download fro free at: http://cnx.org/contents/[email protected]:1/Preface.
