Lab07 Polynomial Graphs and Complex Numbers
- Author:
- Mr.Johnston, byui, mcjmath
- Topic:
- Complex Numbers, Numbers
1) Zeros of a Polynomial
Use the equation of the polynomial function and the graph provided in the applet below.
2) Alternative Methods of Finding Polynomial Zeros
Watch Mr. McLogan find the zeros of the cubic polynomial using synthetic division.
An alternative method is to multiply the factors to get a quadratic expression and then use long division to extract both roots at the same time.
3) Graphs of Complex Numbers
Watch Theschoolofchuck's video below until time 4:00 with the volume muted.
4) The Mandelbrot Set
"More precisely, the Mandelbrot set is the set of values of c in thecomplex plane for which the orbit of 0 under iteration of the complex quadratic polynomial
remains bounded.[1]" Read more on Wikipedia!
This graph uses a recursive formula to generate the points of the graph. It says, to find a point, square the previous point and add on the complex number, c.
Explore the applet by moving point c (now at the origin). As discussed in the video above, this is not on an (x, y) real number coordinate plane but instead on a (real, complex) coordinate plane.