Alg2 2.9 Notes.notebook
October 01, 2012
2­9 Operations with Complex Numbers
Last Night's:
1. The table shows the prices of an ice cream cake, depending on its side. Find a quadratic model for the cost of an ice cream cake, given the diameter. Then use the model to predict the cost of an ice cream cake with a diameter of 18 in.
For Today:
Warm­up Answers
Alg2 2.9 Notes.notebook
October 01, 2012
2­9 Operations with Complex Numbers
Perform operations with complex numbers. Generating Fractals (by performing operations on complex numbers.)
I. Graphing Complex Numbers
1) Graph each complex number
Alg2 2.9 Notes.notebook
October 01, 2012
What does the absolute value mean?
II. Determining Absolute Value
2) Find each absolute value.
A. |3 + 5i|
B. |–13|
C. |–7i|
Alg2 2.9 Notes.notebook
October 01, 2012
III. Adding & Subtracting Complex #
3) Add or subtract, leaving answer as a + bi
a. (4 + 2i) + (–6 – 7i)
b. (1 – 3i) + (–1 + 3i)
c. (5 –2i) – (–2 –3i)
IV. Adding on the Complex Plane
*parallelogram method, (triangular method in pre­calculus)
4) Find (3 – i) + (2 + 3i) by graphing.
Step 1 Graph 3 – i and 2 + 3i on the complex plane. Connect each of these numbers to the origin with a line segment.
Step 2 Draw a parallelogram that has these two line segments as sides. The vertex that is opposite the origin represents the sum of the two complex numbers, 5 + 2i. Therefore, (3 – i) + (2 + 3i) = 5 + 2i.
Alg2 2.9 Notes.notebook
October 01, 2012
V. Multiplying Complex Numbers
5) Multiply the following complex numbers
a. (–5i)(6i)
b. –2i(2 – 4i)
c. (3 + 6i)(4 – i)
d. (2 + 9i)(2 – 9i)
Use i2 = –1
VI. Powers of i
Notice the repeating pattern in each row of the table. The pattern allows you to express any power of i as one of four possible values: i, ­1, ­i, or 1. 6) Simlify
a. –6i14
6
b. i63 ­i
Alg2 2.9 Notes.notebook
October 01, 2012
VII. Dividing Complex Numbers
7) Dividing Complex Numbers
8) Simplify
a.
b.
Alg2 2.9 Notes.notebook
October 01, 2012
Cool!!!!
Complex numbers provide a way of generating Pythagorean triples.
(2 + i)2 = 3 + 4i (3, 4, 5)
(3 + i)2 = 8 + 6i (6, 8, 10)
(4 + i)2 = 15 + 8i (8, 15, 17) Oh, you can do this all on your calculator, by the way...
Say you want to find out (2 + i)2.
1. Press MODE
2. Select a+bi
3. Back to homescreen
4. Type (2 + [2nd] i) ^2
Alg2 2.9 Notes.notebook
October 01, 2012
2.9 p.130 #3­35 odds, 36, 55, 63, 73, 83, 84, 93, 95, 102, 105, 106, 117