1. Rationalizing Imaginary and Complex Denominators
Math 2 Unit 1 Lesson 3

2. Make copies of… Complex Numbers Review.doc
Rationalizing Complex Denominators GO.docx
Kuta-Rationalizing Imaginary Denominators.pdf

3. GPS Standard MM2N1b- Write complex numbers in the form a + bi
MM2N1c- Add, subtract, multiply, and divide complex numbers
MM2N1d- Simplify expressions involving complex numbers

4. Essential Question How do I rationalize pure imaginary denominators?
How do I rationalize complex denominators?

5. Things Not Allowed in a Denominator
Negative sign
Radical
Fractional Exponent
Complex Number
Each one of these must be adjusted out of the problem.

6. Pure Imaginary Denominators
1.) Multiply top and bottom by -i
2.) Change all i2 to -1
3.) Simplify
4.) Make sure you are in standard form

7. Example 1

8. Test Prep Example
Simplify 2 + i i
A) -2i
B) 2i
C) 1 – 2i
D) 1 + 2i

9. Test Prep Example Simplify 1/(2i) over the set of complex numbers.
A) –i/2
B) 2i
C) -2i/1
D) 2i/4i

10. Complex Denominators
1.) Multiply top and bottom by complex conjugate off denominator. Complex conjugate means you change the sign between the two terms.
2.) Change i2 to -1
3.) Simplify and combine like terms
4.) Make sure you are in standard form

11. Examples

12. Test Prep Example Find the complex conjugate of -8 + i A) 8 – i
B) 8 + i
C) -8 – i
D) i - 8

13. Test Prep Example The complex conjugate of 3i + 2 is A) -3i B) 3i
C) 3i – 2
D) -3i + 2

14. Test Prep Example
Simplify the expression
1 + i 1 – i i 1
1 + i
1 – i

15. Test Prep Example Perform the indicated operation. 6 – 2i = 5 + 3i

16. Test Prep Example Which expression is equivalent to 12 – 5i ? 2 – i
A) 19 – 22 i
B) i
C) 19 – 22 i
A) 29 – 2 i

17. Complete Assignment
Kuta-Rationalizing Imaginary Denominators.pdf

18. Complete Assignment
Pg. 13: #27-34
Pg. 14: #22-31