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Section 2.2 The Complex Numbers.

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Presentation on theme: "Section 2.2 The Complex Numbers."— Presentation transcript:

1 Section 2.2 The Complex Numbers

2 Imaginary Numbers Invented in order to find the square root of a negative number. Imaginary numbers are numbers that can be written using i.

3 Imaginary Numbers By definition the following new number was created:
Imaginary Unit Which means. . .

4 Square Root of Negative Number
Caution: This rule should be used before applying any other rules for radicals.

5 Complex Number System Mathematicians invented the complex number system in order to make it possible to solve all quadratic equations. What is a complex number? A real number plus an imaginary number

6 Complex Number- is an expression of the form a + bi where a and b are real numbers and
2 parts of the definition a + bi 1. 2. By definition . . . Real Part Imaginary Part Standard Form

7 Adding/Subtracting Complex Numbers
** Procedure is the same as adding and subtracting like terms ** ex. 3x + 5x ex w – 12 – 4w 8x w To Add/Subtract Complex Numbers 1. Add/Subtract the real parts and add/subtract imaginary parts

8 Multiplying and Dividing Square Roots
Rule when a and b are positive . . .

9 Multiplying and Dividing Square Roots
This rule DOES NOT apply for negative numbers. NO. . . NO. . . NO. . . NO!

10 Multiplication of Complex Numbers
Use FOIL (like multiplying binomials) Remember . . .


12 Dividing Complex Numbers
Complex Conjugate- Conjugate of the divisor is used to find the quotient of two complex numbers in standard form. Conjugate of a+bi is a-bi Conjugate of i is -i


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