Complex Operations
Presentation
•
Mathematics
•
10th - 12th Grade
•
Medium
Lauren Hall
Used 3+ times
FREE Resource
14 Slides • 24 Questions
1
Complex Operations
Mrs. Hall
Algebra II
8/26/2022
2
First, please answer the following questions about graphs!
3
Multiple Select
x-intercepts are also called:
Choose ALL that apply!
Solutions
Roots
Zeros
Parabolas
Puppies
4
Multiple Choice
Given a graph, how can you find the "solutions" to a quadratic?
Call a friend
Solutions are where the quadratic crosses the y-axis
Solutions are where the quadratic crosses the x-axis
Solutions come from the highest or lowest point of a parabola
5
Multiple Choice
What are the solutions, zeros, or x-intercepts of the graph?
(-4,0) and (0,0)
(0,0) and (4,0)
(-2,-2)
None
6
Multiple Choice
What are the real roots (solutions) of the quadratic y = 2x2+4x+5
(−1, 3)
(0,5)
(5,0)
(3,-1)
No real roots
7
Multiple Choice
8
Next, please answer the next FEW questions using the quadratic formula!
9
Multiple Choice
The first step in solving quadratic equations is to . . .
Find a, b, & c
Set the equation =0
use quadratic formula
Cheat
10
Multiple Select
Choose the correct values for a, b, and c.
4x2−5x = 9
a = 4
b = 5
c = 9
b = -5
c = -9
11
Multiple Choice
Identify a, b and c in the quadratic equation: 2x2−3x−5=0
a = 2 , b = 3, c = -5
a = 2, b = -3, c = 5
a = 2, b = -3, c = -5
a = -2, b = 3, c = 5
12
Multiple Choice
x2−4x−7=0
Which example below uses the quadratic formula correctly?
x=2(1)−(4)±(−4)2−4(1)(−7)
x=2(1)−(−4)±(−4)2−4(1)(−7)
x=2(1)−(−4)±(−4)2−4(1)(7)
13
Multiple Choice
What is the discriminant of x2+3x−4=0
25
0
-25
-13
14
Multiple Choice
Solve using the quadratic formula:
x2+4x+3=0
x = 1 and -3
x = -1 and -3
x = -1 and 3
x = 1 and 3
15
Multiple Choice
2p2 - 2p - 55 = 5
16
Multiple Choice
Solve the following equation.
x2+10x+35=0
−5±2i5
−5±i5
−5±2i10
−5±i10
17
Multiple Choice
Solve for x:
3x2 - 6x + 6 = 0
x = 1 ± i
x = 3, -6
1±i 3
Error
18
Complex Numbers (Operations)
Today, you will learn how to add, subtract, and multiply complex numbers!
19
Complex Number
A complex number has the form a + bi, where a is the real component and b is the imaginary component.
Ex.
6 - 3i
0 + 5i
8 + 0i
-3 + 7i
20
Operations with Complex Numbers
Operations with complex numbers are similar to expressions with variables. You can combine real components with each other and imaginary components with each other.
When multiplying imaginary components, you add exponents, similar to multiplying variables.
21
Just combine like terms! The "real" parts, the -2 and 1, combine to make -1 and the "complex" parts 5i and -7i, combine to get -2i.
Simplify
(-2 + 5i) + (1 - 7i)
22
Complete subtraction problems the same way! However, don't forget to distribute the negative to every term in the set of parenthesis.
This is where the +4 - 1i comes from in the 2nd step.
Simplify
(6 + 3i) - (-4 + 1i)
23
Multiple Choice
(4 + 7i) + (8 - 2i)=
34i
28 + 6i
12 + 5i
-4 + 9i
24
Multiple Choice
(3 - 2i) - (4 - 2i) =
-1 + 0i
7 - 4i
1 - 2i
-i
25
Multiple Choice
(5 + 8i) + (6 - 10i)
-1 - 18i
11 - 2i
13 - 4i
-20i
26
Multiple Choice
(-9 - 5i) - (2 - 7i)
-40 + 14i
-7 - 12i
-59i
-11 + 2i
27
Multiply the same way you would basic binomials! There is just ONE extra step...
Multiplying Complex Numbers
28
When multiplying complex...
It is the same method as multiplying binomials!
You can use the foil method or the box method!
HOWEVER. When multiplying binomials, you have an x2 in the problem... You cannot leave "i2" in the problem... i2 = -1... so we replace that part with a -1 and THEN combine like terms!
29
FOIL METHOD - watch as many times as you need to!
30
BOX METHOD - watch as many times as you need to!
(This is the same problem as the previous slide)
31
One More ~*Special*~ problem
32
Multiple Choice
33
Multiple Choice
Simplify: 2i(4 + 3i)
−6 + 8i
6 + 8i
−6i + 8i
−1 + 8i
34
Multiple Choice
Simplify: 3i(3i−4)
−9 −12i
9i−12i
9−12i
−9+12i
35
Multiple Choice
Simplify: (−2 + 7i)(4 − 2i)
6+ 32i
−6 + 32i
22+32i
6 + 24i
36
Multiple Choice
(5−i)2
15-8i
36
24+10i
24-10i
37
Multiple Choice
(7−5i)(7+5i)
74
75
74+i
75-i
38
YAY!
You did it :) Great Job!!! Now grab the coloring sheet or maze to work on until the end of class!
I hope you tried... if you didn't try... that's disappointing. Because surprise! This is for an accuracy grade! Love y'all and see you Monday! ✌️
Complex Operations
Mrs. Hall
Algebra II
8/26/2022
Show answer
Auto Play
Slide 1 / 38
SLIDE
Similar Resources on Wayground
36 questions
Unit Circle Trig Practice
Presentation
•
9th - 12th Grade
31 questions
Rational Exponents & Radicals (Laws of Exponents Review)
Presentation
•
9th - 12th Grade
34 questions
Reading a Pay Stub
Presentation
•
10th - 12th Grade
33 questions
Amortization
Presentation
•
9th - 12th Grade
30 questions
Add and Subtract Integers Lesson 1 (from 3/2)
Presentation
•
9th - 12th Grade
34 questions
Graphs of Logarithmic Functions
Presentation
•
11th Grade
35 questions
Radians and Review
Presentation
•
10th - 12th Grade
35 questions
Naming Ionic Compounds
Presentation
•
10th - 12th Grade
Popular Resources on Wayground
24 questions
PBIS-HGMS Day 10
Quiz
•
6th - 8th Grade
10 questions
HCS SCI 03 Summer School Review 3
Quiz
•
3rd Grade
11 questions
Home Scope
Quiz
•
7th - 8th Grade
15 questions
HCS SCI 05 Summer School Assessment 3 Review
Quiz
•
5th Grade
35 questions
Lufkin Road Middle School Student Handbook & Policies Assessment
Quiz
•
7th Grade
18 questions
Geo 11.3 Area of Circles and Sectors
Quiz
•
9th - 11th Grade