Daily Check: Perform the indicated operation. Find the area and perimeter of the box. 3. Perimeter = ____ 4. Area = ____ 2x+1 2x-3

Homework Review

CCGPS Analytic Geometry Day 32 ( ) UNIT QUESTION: In what ways can algebraic methods be used in problem solving? Standard: MCC9-12.N.RN.1-3, N.CN.1-3, A.APR.1 Today’s Question: How do we take the square root of negative numbers? Standard: MCC9-12..N.CN.1-3

You can't take the square root of a negative number, right? When we were young and still in Math I, no numbers that, when multiplied by themselves, gave us a negative answer. Squaring a negative number always gives you a positive. (-1)² = 1. (-2)² = 4 (-3)² = 9

So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary” So, does really exist?

Examples of how we use

1.3 Powers of i and Complex Operations

*For larger exponents, divide the exponent by 4, then use the remainder as your exponent instead. Example:

Complex Numbers A complex number has a real part & an imaginary part. Standard form is: Real part Imaginary part Example: 5+4i

The Complex Plane Imaginary Axis Real Axis

Graphing in the complex plane

Adding and Subtracting Add or subtract the real parts, and then, add or subtract the imaginary parts. Ex: Ex:

Your Turn!

Multiplying Treat the i’s like variables, then change any that are not to the first power Ex: Ex:

Your Turn!

Conjugates: Two complex numbers of the form a + bi and a – bi are complex conjugates. The product is always a real number Ex:

Conjugates: Two complex numbers of the form a + bi and a – bi are complex conjugates. The product is always a real number

Dividing Complex Numbers

Conjugates: Two complex numbers of the form a + bi and a – bi are complex conjugates. The product is always a real number

Dividing Complex Numbers Multiply the numerator and denominator by the conjugate of the denominator. Simplify completely.

Writing in Standard Form

Your Turn!

Assignment Complex Numbers Practice WS