Groups Today Group 1: Myles, Kaitlyn, Victoria Group 2: Matthew, William, Emily Group 3: Darius, Vanessa Group 4: Jorge, Mariana, Anthony Group 5: Ryan, Julio, Moises Group 6: Anthony G., Le’ona, Ariadny

Complex Numbers

Imaginary Unit Until now, you have always been told that you can’t take the square root of a negative number. If you use imaginary units, you can! The imaginary unit is ¡ ¡= It is used to write the square root of a negative number.

Property of the square root of negative numbers If r is a positive real number, then Examples:

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

Examples

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

The Complex plane Real Axis Imaginary Axis

Graphing in the complex plane

Adding and Subtracting (add or subtract the real parts, then add or subtract the imaginary parts) Ex: Ex: Ex:

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

Partner Showdown You will complete the problem on their own, and reveal the answer to one-another at the same time. If your group all has the same answer, you may move on. If you do not, you must discuss any errors and work together to clear-up any misunderstandings before moving on.

Next class You will have a quiz on this material next class. Be sure to complete your homework!

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