Warm-up #34 Tuesday 12/8. Lesson 3.11 Imaginary Number and Complex Number.

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Presentation transcript:

Warm-up #34 Tuesday 12/8

Lesson 3.11 Imaginary Number and Complex Number

Imaginary Number An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit “i” Example: 5i or -6i

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

Simplify

Example

The “Imaginary Rule”

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

Examples

Complex Numbers A complex number has a real part & an imaginary part. Standard form is: Real part Imaginary part Example: 5+4i, 4-3i

Identify Real Part and Imaginary Part Complex Numbers Real PartImaginary Part 6 – 6i 7+ 3i -13 – 5i

1. (-2 + 3i) + (-2 – 4i) Adding and Subtracting: add or subtract the real parts, then add or subtract the imaginary parts

1. (-9 + i) + (-12 – 6i) Adding and Subtracting: add or subtract the real parts, then add or subtract the imaginary parts

Multiplying: Treat the i’s like variables, then apply the “imaginary rule” 1. (-5 + 3i)(2 – 3i)

Multiplying: Treat the i’s like variables, then apply the “imaginary rule” 1. (-7 + 2i)(6 – 8i)

Warm-up #33 Monday, 12/7

Homework Monday, 12/7 Chapter 3 study guide Note: notebook check and homework log

Extra Credit for NO MISSING HW Jacob A, Henry, Nicole A, Angela, Chloe, Jacob, Alex E, Thomas E, Emiliano, Isabella G, Reed, Nicholas H, Tommy, Giorgia, Rey, Sam, Max, Tanner, Lukas, Evan, Poppy, Nicole W, Meg Last day to turn in late assignment for Chapter 3 is on Tuesday, Dec 8.