Rationalizing Imaginary and Complex Denominators Math 2 Unit 1 Lesson 3

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

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

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

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

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

Example 1

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

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

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

Examples

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

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

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

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

Test Prep Example Which expression is equivalent to 12 – 5i ? 2 – i A) 19 – 22 i 3 3 B) 29 + 2 i 3 3 C) 19 – 22 i 5 5 A) 29 – 2 i 5 5

Complete Assignment Kuta-Rationalizing Imaginary Denominators.pdf

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