Your SlideShare is downloading.
×

×

Saving this for later?
Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.

Text the download link to your phone

Standard text messaging rates apply

Like this presentation? Why not share!

1,633

Published on

No Downloads

Total Views

1,633

On Slideshare

0

From Embeds

0

Number of Embeds

1

Shares

0

Downloads

79

Comments

0

Likes

1

No embeds

No notes for slide

- 1. 4.8 COMPLEX NUMBERSPart 1: Introduction to Complex and ImaginaryNumbers
- 2. REAL NUMBERS See Page 12 in Textbook
- 3. COMPLEX NUMBERS The set of Real Numbers is a subset of a larger set of numbers called Complex Numbers The complex numbers are based on a number whose square is –1 The imaginary unit i is the complex number whose square is –1 .
- 4. SQUARE ROOT OF A NEGATIVE REAL NUMBER For any real number a,
- 5. EXAMPLE: SIMPLIFY EACH NUMBER BY USINGTHE IMAGINARY NUMBER
- 6. EXAMPLE: SIMPLIFY EACH NUMBER BY USINGTHE IMAGINARY NUMBER
- 7. EXAMPLE: SIMPLIFY EACH NUMBER BY USINGTHE IMAGINARY NUMBER
- 8. IMAGINARY NUMBERS An imaginary number is any number of the form a + bi, where a and b are real numbers and b ≠ 0. a + bi ↑ ↑ Real Imaginary Part Part If b = 0, then the number is a real number If a = 0 and b ≠ 0, then the number is a pure imaginary number
- 9. COMPLEX NUMBERS Imaginary numbers and real numbers make up the set of complex numbers
- 10. THE QUADRATIC FORMULA Every quadratic equation has complex number solutions (that are sometimes real numbers). We can use and the quadratic formula to solve all quadratic equations.
- 11. FIND ALL SOLUTIONS TO EACH QUADRATICEQUATION
- 12. FIND ALL SOLUTIONS TO EACH QUADRATICEQUATION
- 13. GRAPHING COMPLEX NUMBERS In the complex number plane, The x – axis represents the real part The y – axis represents the imaginary part The point (a, b) represents the complex number a + bi The absolute value of a complex number is its distance from the origin in the complex plane.
- 14. EXAMPLE: WHAT ARE THE GRAPH ANDABSOLUTE VALUE OF EACH NUMBER?
- 15. EXAMPLE: WHAT ARE THE GRAPH ANDABSOLUTE VALUE OF EACH NUMBER?
- 16. HOMEWORK P253 #1, 2, 8 – 17 all, 39 – 44 all

Be the first to comment