Addition and Subtraction
| Site: | Clare-Gladwin RESD |
| Course: | Michigan Algebra II KHauck |
| Book: | Addition and Subtraction |
| Printed by: | Guest user |
| Date: | Tuesday, November 26, 2024, 12:49 AM |
Description
Addition & Subtraction
In the last unit, polynomials had complex roots of the form: a + bi , where 
. A number of the form: a + bi , where a and b are real numbers and , is called a complex number. Here are some examples:
4 + 3i
6i - 2
4i (when a = 0)
-16 (when b = 0)
Addition
In Algebra, complex numbers operate similarly to variable expressions. Adding complex numbers operate similarly to adding polynomials. When adding complex numbers, combine like terms.
Example Simplify the following expression
Step 1. Clear the parentheses.
Step 2. Combine like terms.
Step 3. Add like terms.
Subtraction
Since complex numbers operate similarly to polynomial expressions, when subtracting complex numbers change the sign of the terms being subtracted using the Distributive Property. Clear the parentheses. Combine like terms.
Example 1 Simplify the following expression
Step 1. Change the signs of the second complex number.
Step 2. Clear the parentheses.
Step 3. Combine like terms.
Example 2
Simplify the following expression
Step 1. Simplify the radicals using imaginary numbers.
Step 2. Change the signs of the second complex number and clear the parentheses.
Step 3. Combine like terms and simplify.
To learn more about adding and subtracting complex numbers, select the following link:
Video Lesson
To learn how to add and subtract complex numbers select the following link:
Practice
Add and Subtract Complex Worksheet*Note: If Google Docs displays "Sorry, we were unable to retrieve the document for viewing." refresh your browser.
Answer Key
Add and Subtract Complex Numbers Key*Note: If Google Docs displays "Sorry, we were unable to retrieve the document for viewing." refresh your browser.
Sources
Sources used in this book:
Embracing Mathematics, Assessment & Technology in High Schools; a Michigan Mathematics & Science Partnership Grant Project
Guido, Tami. "Practicing Arithmetic of Complex." http://www.regentsprep.org/Regents/mathb/3c2/practicepage.htm (accessed 8/10/2010).
Holt, Rinehart & Winston, "Quadratic Functions." http://my.hrw.com/math06_07/nsmedia/homework_help/alg2/alg2_ch05_09_homeworkhelp.html (accessed 8/10/2010).
Knaust, Helmut. "Complex Numbers." http://www.sosmath.com/algebra/factor/fac09/fac09.html (accessed 8/10/2010).
Palmitesso, Tami. "Adding and Subtracting Complex Numbers." http://www.regentsprep.org/Regents/math/algtrig/ATO6/lessonadd.htm (accessed 8/10/2010).