The Complex Numbers

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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. 3 8w 12 4w
• 8x -9 4w
• 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 abi is a-bi
• Conjugate of i is -i

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