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Section 2.2

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

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Section 2.2

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  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 StandardForm

  7. 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

  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 . . .

  11. 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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