1 / 8

Solve the quadratic equation x 2 + 1 = 0. Solving for x , gives x 2 = – 1

Bell Work #1. Solve the quadratic equation x 2 + 1 = 0. Solving for x , gives x 2 = – 1. We make the following definition:. Complex Numbers. Note that squaring both sides yields: therefore and so and. And so on….

gallia
Download Presentation

Solve the quadratic equation x 2 + 1 = 0. Solving for x , gives x 2 = – 1

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. Bell Work #1 Solve the quadratic equation x2 + 1 = 0. Solving for x , gives x2 = – 1 We make the following definition:

  2. Complex Numbers Note that squaring both sides yields: therefore and so and And so on…

  3. Real numbers and imaginary numbers are subsets of the set of complex numbers. Complex Numbers Imaginary Numbers Real Numbers

  4. Definition of a Complex Number If a and b are real numbers, the number a + bi is a complex number, and it is said to be written in standard form. If b = 0, the number a + bi = a is a real number. If a = 0, the number a + biis called an imaginary number. Write the complex number in standard form

  5. Addition and Subtraction of Complex Numbers If a + bi and c +diare two complex numbers written in standard form Sum: Difference:

  6. Perform the subtraction and write the answer in standard form. ( 3 + 2i ) – ( 6 + 13i ) 3 + 2i – 6 – 13i –3 – 11i 4

  7. Multiplying Complex Numbers Multiplying complex numbers is similar to multiplying polynomials and combining like terms. Perform the operation and write the result in standard form. ( 6 – 2i )( 2 – 3i ) F O I L 12 – 18i – 4i + 6i2 12 – 22i + 6 ( -1 ) 6 – 22i

  8. Consider ( 3 + 2i )( 3 – 2i ) 9 – 6i + 6i – 4i2 9 – 4( -1 ) 9 + 4 13 This is a real number. The product of two complex numbers can be a real number.

More Related