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4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
4.8 complex numbers
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4.8 complex numbers

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  • 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

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