Videos Primitive tribe can count to 2 http://www.youtube.com/watch?v=BDIv7r-X2kk

Section 2.4 Complex Numbers

{1, 2, 3, 4,…} How many natural numbers are there? Real Number System

{0, 1, 2, 3, 4,…} Real Number System How many whole numbers are there? Natural Whole

How many integers numbers are there? Real Number System Natural {...-3, -2, -1, 0, 1, 2, 3, …} How many integers numbers are there? Whole Integers

Real Number System Fractions How many rational numbers are there? Natural Whole Integers Rational

Real Number System How many irrational numbers are there? Natural Whole Integers Irrational Rational

Real Number System Each set is a subset of the Real Number System. Natural Each set is a subset of the Real Number System. The union of all these sets forms the real number system. The number line is our model for the real number system. Whole Integers Irrational Rational Real Numbers

Definition of Square Root If a2 = n then a is a square root of n. 42 = (4)(4) = 16  4 is a square root of 16 (-4)2 = (-4)(-4) = 16  -4 is a square root of 16

What’s the square root of -16? Whatever it is, it is not on the real number line.

Definition of i The number i is such that Imaginary Unit

If you square a radical you get the radicand 2 2 Whenever you have i2 the next turn you will have -1 and no i.

Complex Numbers REAL Imaginary Complex

Definition of a Complex Number If a and b are real numbers, the number a + bi is a complex number, and it is said to be written in standard form. If b = 0 then the number a + bi = a is a real number. If b ≠ 0, then the number a + bi is called an imaginary number. A number of the form bi, where b ≠ 0 is called a pure imaginary number.

Examples

Equality of Complex numbers If a + bi = c + di, then a = c and b = d.

Is a negative times a negative always positive? Trick question. This is not a negative times a negative.

Example

Example Cancel the i factor

Add Collect like terms.

First distribute the negative sign. Subtract Now collect like terms.

Multiplication F O I L

Multiply by the conjugate factor. Write in the form 2 Multiply by the conjugate factor.

Powers of i Anything other than 0 raised to the 0 is 1. Anything raised to the 1 is itself.

Find

Use the Quadratic Formula What does this mean about the graph of this Parabola?

H Dub 2.4 Pg. 167 #5-81EOO

Simplify each expression. Express your answer in form. F-O-I-L Recall i2=-1 Combine like terms. Combine like terms.