Section 3.2 Complex Numbers Honors Algebra 2 Section 3.2 Complex Numbers

https://www.youtube.com/watch?v=OFSrINhfNsQ

Do you remember when you were told there was no Santa Claus?

When you learned about real numbers, you probably assumed that’s ALL numbers There is a bigger world of numbers out there!!

Complex numbers includes the set of real numbers and the set of imaginary numbers

The standard form of a complex number is 𝒂+𝒃𝒊 When b=0, the number is real When a=0, the number is pure imaginary Think of these as purebreds

The equation 𝑥 2 =−4 has no real solutions. The solutions to this equation are imaginary. Imaginary unit-(i) the square root of -1 ( −1 ) 𝑖 2 =−1 i can be used to find the square root of a negative number

All other complex numbers have a real part and an imaginary part Think of them as mutts

To simplify a pure complex number, take any perfect square factors and -1 out of the radical −75 −1∙25∙3 5𝑖 3 Try these: 1. −36 2. −400 3. −8 4. −27

Equal complex numbers If 5+𝑥𝑖=𝑦−2𝑖, what do you think x and y are equal to?

Adding and subtracting complex numbers is easy! Add or subtract the “a” terms Add or subtract the “b” terms Simplify the following: (6−2𝑖) +(11+8𝑖) 2. 10−𝑖 −(3+5𝑖)

When multiplying complex numbers: (You already know how to multiply to real numbers) Real times imaginary One term x two terms- use distributive prop. Two terms x two terms- use FOIL

Write answers in the form 𝑎+𝑏𝑖 Never leave 𝑖 2 in your final answer! Try these: 1. 5𝑖(8−3𝑖) 2. 3+4𝑖 6−7𝑖 3. (3+𝑖)(4−𝑖)

Solving quadratic equations when b=0 Isolate the variable Take the square root of each side. Don’t forget ±. Try these: 1. 35 𝑥 2 =−105 2. 𝑥 2 =−45 3. 2𝑥 2 −8=−24

Finding Zeros of a Quadratic Function Replace f(x) with zero Solve 1. Find the zeros of 𝑓 𝑥 =6 𝑥 2 +42 2. Find the zeros of 𝑓 𝑥 = 2𝑥 2 +2

Assignment #10 Pg. 108 #1-43 odd, 49-61 odd