Complex Numbers

Class Opener:  

Quiz: 13 multiple choice questions Input answers in on the clicker Should be very easy.

ACT Class Opener: http://sbstjohn.com/QODWebSite/PlaneGeom/plane_1213_f016.htm http://sbstjohn.com/QODWebSite/PlaneGeom/plane_1213_f068a.htm http://sbstjohn.com/QODWebSite/Trigonom/trig_1213_f015.htm

Re-Do Partner Up and re-do the top 5 missed questions from the quiz yesterday. 7 ,8, 9, 12, 13

Class Opener:  

Definition of pure imaginary numbers: Any positive real number b, where i is the imaginary unit and bi is called the pure imaginary number.

it is a symbol for a specific number Definition of pure imaginary numbers: i is not a variable it is a symbol for a specific number

Simplify each expression.

Simplify each expression. Remember Remember

Simplify. To figure out where we are in the cycle divide the exponent by 4 and look at the remainder.

Divide the exponent by 4 and look at the remainder. Simplify. Divide the exponent by 4 and look at the remainder.

Divide the exponent by 4 and look at the remainder. Simplify. Divide the exponent by 4 and look at the remainder.

Divide the exponent by 4 and look at the remainder. Simplify. Divide the exponent by 4 and look at the remainder.

Definition of Complex Numbers Any number in form a+bi, where a and b are real numbers and i is imaginary unit.

Definition of Equal Complex Numbers Two complex numbers are equal if their real parts are equal and their imaginary parts are equal. If a + bi = c + di, then a = c and b = d

When adding or subtracting complex numbers, combine like terms.

Simplify.

Simplify.

Multiplying complex numbers. To multiply complex numbers, you use the same procedure as multiplying polynomials.

Simplify. F O I L

Simplify. F O I L

The Habitat for humanity project utilizes volunteers to help build house for low – income families who might not be able to afford the purchase of a home. At a recent site, Habitat workers built a small storage shed attached to the house. The electrical blueprint for the shed called for two AC circuits connected in series with a total voltage of 220 volts. One of the circuits must have an impedance of 7-10j ohms, and the other needs to have an impedance of 9+5j ohms. According to the building codes, the impedance cannot exceed 20-5j ohms. Will the circuits, as designed, meet the code?

Complex Conjugates:  

Multiplying Conjugates Multiply (3 – 5i) by its complex conjugate.

Student Check:  

Quotient of Complex Numbers  

Student Check:  

Graphing Complex Numbers: How do we graph the following: 2 + 3i -1 + 2i -3i

Skip Vocabulary Section Student Practice: Pg. 137 – 138 #1 – 76 odd Skip Vocabulary Section