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Section 2.2 The Complex Numbers

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

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**Imaginary Numbers By definition the following new number was created:**

Imaginary Unit Which means. . .

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**Square Root of Negative Number**

Caution: This rule should be used before applying any other rules for radicals.

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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

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**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

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**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

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**Multiplying and Dividing Square Roots**

Rule when a and b are positive . . .

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**Multiplying and Dividing Square Roots**

This rule DOES NOT apply for negative numbers. NO. . . NO. . . NO. . . NO!

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**Multiplication of Complex Numbers**

Use FOIL (like multiplying binomials) Remember . . .

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**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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