Complex+Numbers

=Complex Numbers=

==**Depict imaginary solutions.** == 2. You can see from your graph that here are no real number values of //x// such that //y = 0.// Use the quadratic formula to solve the equation 0 = x^2 + x + 1. Recall that we defined //i// to represent the square root of -1. ==**The Complex Plane and Addition of Complex Numbers** == Complex numbers have a real part //a// and an imaginary part //b: a+bi//. They can be graphed on the complex plane with the horizontal real axis and the vertical imaginary axis. 2. Algebraically add (3+2i)+(5-2i) by combining like terms. 3. Identify the sum on the graph.
 * 1. Sketch a graph of the parabola y = x^2 + x + 1 at right.
 * You may draw your graph and write your solution by hand, scan your work, and upload the file into the cell below.
 * Include the names of group members participating in this section of the lesson. ||
 * 1. Use the ordered pair (3, 2) to graph 3+2i and the ordered pair (5, -2) to graph 5-2i on the same axes.
 * You may draw your graph and write your sum by hand, scan your work, and upload the file into the cell below.
 * Include the names of group members participating in this section of the lesson. ||

**The Complex Plane and Multiplication of Complex Numbers**
Complex numbers have a real part //a// and an imaginary part //b: a+bi//. They can be graphed on the complex plane with the horizontal real axis and the vertical imaginary axis. 2. Algebraically multiply (3+2i)+(5-2i) by "F-O-I-L"-ing and combining like terms. 3. Identify the product on the graph.
 * 1. Use the ordered pair (3, 2) to graph 3+2i and the ordered pair (5, -2) to graph 5-2i on the same axes.
 * You may draw your graph and write your sum by hand, scan your work, and upload the file into the cell below.
 * Include the names of group members participating in this section of the lesson. ||

**Complex Conjugates**
==** Complex numbers have a real part //a// and an imaginary part //b: a+bi//. They can be graphed on the complex plane with the horizontal real axis and the vertical imaginary axis. ** == 2. Algebraically multiply (3+2i)+(3-2i) by "F-O-I-L"-ing and combining like terms. 3. Identify the product on the graph.
 * 1. Use the ordered pair (3, 2) to graph 3+2i and the ordered pair (3, -2) to graph 3-2i on the same axes.
 * You may draw your graph and write your sum by hand, scan your work, and upload the file into the cell below.
 * Include the names of group members participating in this section of the lesson. ||

**Who Developed the Operations of Complex Numbers?**
Identify at least one significant mathematician associated with the development of the complex numbers. (Raphael Bombelli is one such character.) Consider using the following site: []
 * 1) When and where did your mathematician live?
 * 2) What was his/her contribution to the development of the complex numbers?

Use the guidelines provided in class to collaborate using Google Docs to create an attractive trading card (half of an 8.5"x11" sheet of paper) including a picture of your mathematician and a brief synopsis of his/her life. Cite any sources used and identify group members participating in this section of the lesson.