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Warm Up  Divide the complex number 3 – 2i 1 + i  Multiply the complex number (3 -2i)(1+i)

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Presentation on theme: "Warm Up  Divide the complex number 3 – 2i 1 + i  Multiply the complex number (3 -2i)(1+i)"— Presentation transcript:

1 Warm Up  Divide the complex number 3 – 2i 1 + i  Multiply the complex number (3 -2i)(1+i)

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8 Math IV Lesson11 Complex numbers 2.5 Essential Question: Standard: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise.

9  The degree of a polynomial with one variable is the largest exponent of that variable.  Root: where the polynomial is equal to zero.  A quadratic factor with no real zeros is said to be prime.

10 The degree of a polynomial with one variable is the largest exponent of that variable.

11 Roots A root is where the polynomial is equal to zero So, a polynomial of degree 3 will have 3 roots (places where the polynomial is equal to zero). A polynomial of degree 4 will have 4 roots. And so on.

12 Example: what are the roots of x 2 - 9? x has a degree of 2, so there will be 2 roots. Let us solve it. We want it to be equal to zero: x = 0 First move the -9 to the other side: x 2 = +9 Then take the square root of both sides: x = ±3 So the roots are -3 and +3

13 A polynomial can be rewritten like this: The factors like (x-r 1 ) are called Linear Factors, because they make a line when you plot them.

14 Polynomials can have complex roots

15 Complex roots always come in pairs Example: x 2 -x+1 Had these roots: iand i You can either have: No complex roots 2complex roots 4 complex roots 6 complex roots …

16 Factoring a polynomial

17 Use the quadratic formula to solve find the zeros of F(x) = x 2 -12x + 26 QUADRATIC FORMULA

18 Homework P144 # 1-4, odd


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