1 / 13

Understanding Complex and Imaginary Numbers in Mathematics

Imaginary numbers were invented to solve the square root of negative numbers, defined using 'i', the imaginary unit. The complex number system allows all quadratic equations to be solvable, represented as a + bi, where 'a' is the real part and 'b' the imaginary part. Adding and subtracting complex numbers involves combining real and imaginary parts separately. Multiplication is done using the FOIL method, while division requires the complex conjugate. Caution should be exercised with rules for radicals concerning negative numbers.

violet-jones
Télécharger la présentation

Understanding Complex and Imaginary Numbers in Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

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 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

More Related