Rationalizing Imaginary and Complex Denominators

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 i2to -1 3.) Simplify 4.) Make sure you are in standard form

Example 1

Test Prep Example • Simplify2 + 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 + i1 – i • i • 1 • 1 + i • 1 – i

Test Prep Example • Perform the indicated operation. 6 – 2i =5 + 3i • 7i 4 • 6 – 22 i5 25 • 9 – 1i4 2 • 12 – 14i17 17

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

Rationalizing Imaginary and Complex Denominators