Section 2.2 The Complex Numbers

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

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

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

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

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

Adding/Subtracting Complex Numbers ** Procedure is the same as adding and subtracting like terms ** ex. 3x + 5x ex. 3 + 8w – 12 – 4w 8x -9 + 4w To Add/Subtract Complex Numbers 1. Add/Subtract the real parts and add/subtract imaginary parts

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

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

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

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