Copyright © 2011 Pearson, Inc. P.6 Complex Numbers.

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Presentation transcript:

Copyright © 2011 Pearson, Inc. P.6 Complex Numbers

Copyright © 2011 Pearson, Inc. Slide P What youll learn about Complex Numbers Operations with Complex Numbers Complex Conjugates and Division Complex Solutions of Quadratic Equations … and why The zeros of polynomials are complex numbers.

Copyright © 2011 Pearson, Inc. Slide P Complex Number A complex number is any number that can be written in the form a + bi, where a and b are real numbers. The real number a is the real part, the real number b is the imaginary part, and a + bi is the standard form.

Copyright © 2011 Pearson, Inc. Slide P Addition and Subtraction of Complex Numbers If a + bi and c + di are two complex numbers, then Sum: (a + bi ) + (c + di ) = (a + c) + (b + d)i, Difference: (a + bi ) – (c + di ) = (a – c) + (b –d)i.

Copyright © 2011 Pearson, Inc. Slide P Example Multiplying Complex Numbers

Copyright © 2011 Pearson, Inc. Slide P Solution

Copyright © 2011 Pearson, Inc. Slide P Complex Conjugate

Copyright © 2011 Pearson, Inc. Slide P Complex Numbers The multiplicative identity for the complex numbers is 1 = 1 + 0i. The multiplicative inverse, or reciprocal, of z = a + bi is

Copyright © 2011 Pearson, Inc. Slide P Example Dividing Complex Numbers

Copyright © 2011 Pearson, Inc. Slide P Solution the complex number in standard form.

Copyright © 2011 Pearson, Inc. Slide P Discriminant of a Quadratic Equation

Copyright © 2011 Pearson, Inc. Slide P Example Solving a Quadratic Equation

Copyright © 2011 Pearson, Inc. Slide P Example Solving a Quadratic Equation

Copyright © 2011 Pearson, Inc. Slide P Quick Review

Copyright © 2011 Pearson, Inc. Slide P Quick Review Solutions

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