Presentation on theme: "Warm Up Divide the complex number 3 – 2i 1 + i Multiply the complex number (3 -2i)(1+i)"— Presentation transcript:
Warm Up Divide the complex number 3 – 2i 1 + i Multiply the complex number (3 -2i)(1+i)
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.
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.
The degree of a polynomial with one variable is the largest exponent of that variable.
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.
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
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.
Polynomials can have complex roots
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 …
Factoring a polynomial
Use the quadratic formula to solve find the zeros of F(x) = x 2 -12x + 26 QUADRATIC FORMULA