1. NOTES 5.7 FLIPVOCABFLIPVOCAB

2. Notes 5.7 Given the fact i 2 = ________ The imaginary number is _____ which equals _____ Complex numbers are written in the form: _______________ Where “a” is a real number and bi is an imaginary number Simplify expression vs. Solving equation FLIPVOCABFLIPVOCAB

3. RootsAxis of Symmetry Rational, Irrational, or Imaginary x = {-5, 2} x = 5 ± x = ± 2i x = -1 ± x = 4 and x = 4 X = 3 ± Complete the chart about roots Rational Irrational Imaginary FLIPVOCABFLIPVOCAB

4. Given ProblemWork Answer (i may be in the answer) i = i2i2 i3i3 i4i4 i7i7 i8i8 i 33 i 103 Simplify numbers with imaginary numbers -i 1 -i 1 FLIPVOCABFLIPVOCAB

5. Complex numbers are written in the form: ___________ Where a is a real number and bi is an imaginary number The complex conjugate is _____________ We will use complex conjugates to simplify division problems where a ______________ _________________ is in the denominator complex number FLIPVOCABFLIPVOCAB

6. Operations with imaginary/complex numbers The 2 nd problem shows complex conjugates being multiplied

7. Division with imaginary/complex numbers Multiply by a form of 1 so value doesn’t change Since the denominator is a binomial, you must multiply by a complex conjugate Since the denominator is a monomial, you must multiply by a monomial form of one Poor form: radical, imaginary, or 0 in denominator!

8. Rationalize the denominator Multiply by a form of 1 We don’t want radicals, i, or zero in the denominator. Simplify:

9. Is 5+i a solution (root/zero) of the function f(x) = x 2 – 10x + 26 ?