Find the quotient. Express your answer in standard form.−5+3i−7−4i\frac{-5+3i}{-7-4i}

2365−4165i\frac{23}{65}-\frac{41}{65}i6523−6541i

Find the quotient. Express your answer in standard form. − 5 + 3 i − 7 − 4 i \frac{-5+3i}{-7-4i}

In this problem, we want to divide these complex numbers and then express our answer in standard form. And here I have negative 5+3i divided by negative 7 minus 4i. So So let's go ahead and start with step 1, which is gonna be to multiply both the top and the bottom by the complex conjugate of the bottom. So since my denominator here is negative 7 minus 4 I, the complex conjugate of that is going to be negative 7+4i because we're reversing the sign of that imaginary part, and we wanna multiply both the top and the bottom by this negative 7+4i. So let's go ahead and foil this out with our numerator. So starting with my first term, I have negative 5 times negative 7, it's going to give me positive 35. And then my outside term, negative 5 times 4 I, is going to give me negative 20 I. Then I have my inside term, 3 I times negative 7, it's going to give me negative 21i. And then my last term, 3i times 4i will give me positive 12i squared. Okay. So looking at my denominator here, if we remember our shortcut that this just becomes a squared plus b squared. Now you can always foil this out, of course, but knowing that these 2 multiplied together just become a squared plus b squared, this is gonna be negative 7 squared plus negative 4 squared, and negative 7 squared is positive 49, plus negative 4 squared is positive 16, and these 2 added together is going to give me 65. So my denominator here is just 65. So we've completed step 1. Now step 2 is to go ahead and combine like terms. And remember we can also simplify this I squared here into a negative one, so this is really just 12 times negative one. Let's go ahead and rewrite this simplifying a little bit. So I have 35 minus 20 I minus 21 I minus 12 because this 12 times negative one all divided by 65. Okay. Now we can go ahead and combine like terms. So on the numerator here, I have 35 and I have a negative 12 and then I also have negative 20i and negative 21i. So let's go ahead and combine those like terms. Now 35 minus 12 is going to give me 23 minus 20 I minus 21 I is negative 41 I. And this is all divided by 65. So step 2 is done as well. We can go ahead and expand our fraction into the real and imaginary parts. So splitting that numerator there, I am left with 23 over 65 minus 41 over 65 I. Okay. So step 3 is done as well. We can simplify fractions to lowest terms, and these are actually already in their lowest terms. Now I know that these fractions look a little bit crazy but we're completely done and this is our solution. Let me know if you have any questions and I'll see you in the next one.

Find the quotient. Express your answer in standard form.−5+3i−7−4i\frac{-5+3i}{-7-4i}

2365−4165i\frac{23}{65}-\frac{41}{65}i6523−6541i

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1. Whole Numbers1h 55m

Multiplying Whole Numbers
46m

Dividing Whole Numbers
21m

Long Division
36m

Exponents
10m

2. Integers1h 7m

Introduction to Integers
16m

Multiplying Integers
24m

Exponential Expressions
10m

Dividing Integers
16m

3. Introduction to Solving Equations and Problem Solving43m

Simplifying Expressions
13m

Translating Word Phrases to Algebraic Expressions
6m

Introduction to Solving Equations
21m

Translating Sentences to Algebraic Equations
2m

4. Fractions1h 29m

Intro To Fractions and Mixed Numbers
44m

Simplifying Fractions
45m

5. Decimals1h 20m

Introduction To Decimals
27m

Rounding Decimals
12m

Adding And Subtracting Decimals
41m

6. Ratio, Proportion, and Percent2h 3m

Ratios and Rates
35m

Proportions
34m

Solving Percent Problems With Equations
16m

Applications of Percent
36m

7. Graphing and Introduction to Statistics40m

Tables
12m

Bar Graphs
3m

Frequency Distributions and Histograms
5m

Line Graphs
14m

Circle Graphs
4m

8. Geometry49m

Square Roots and The Pythagorean Theorem
29m

The Circle
20m

9. Measurement58m

US Units of Length
25m

Metric Units of Length
33m

10. Linear Equations and Inequalities6h 13m

The Distributive Property
17m

Review: Addition and Subtraction Properties of Equality
41m

Review: Multiplication and Division Properties of Equality
30m

Solving Linear Equations
1h 14m

Introduction to Problem Solving
37m

Formulas
21m

Review: Percent Problem Solving
59m

Mixture Problem Solving
43m

Linear Inequalities in One Variable
46m

11. Graphing Linear Equations3h 17m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

Slope-Intercept Form
38m

Point Slope Form
22m

12. Systems of Linear Equations1h 43m

Solving Systems of Linear Equations by Graphing
41m

Solving Systems of Linear Equations by Substitution
15m

Solving Systems of Linear Equations by Elimination
45m

13. Exponents and Polynomials3h 55m

Review: Evaluating Exponents
29m

The Product Rule
10m

Intro to the Power Rules
18m

The Power of a Quotient Rule
18m

Negative Exponents
28m

The Quotient Rule
13m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

Adding and Subtracting Polynomials
20m

Multiplying Polynomials
33m

Special Products
34m

14. Factoring Polynomials2h 42m

Factoring by Greatest Common Factor & Grouping
37m

Factoring Trinomials of the Form x² + bx + c
11m

Factoring Trinomials of the Form ax² + bx + c
37m

Factoring Special Products
20m

Sum & Difference of Cubes
12m

Quadratic Equations & Applications
41m

15. Rational Expressions and Equations3h 13m

Simplifying Rational Expressions
39m

Multiplying And Dividing Rational Expressions
25m

Adding and Subtracting Rational Expressions with Common Denominators
19m

Least Common Denominators
32m

Adding and Subtracting Rational Expressions with Different Denominators
32m

Rational Equations
44m

16. Relations and Functions2h 9m

Introduction to Relations and Functions
57m

Function Notation
15m

Graphing Common Functions
5m

Composition of Functions
24m

Direct & Inverse Variation
27m

17. Inequalities and Absolute Value2h 52m

Set Operations and Compound Inequalities
42m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

Linear Inequalities in Two Variables
28m

Systems of Linear Inequalities
23m

18. Roots, Radicals, and Complex Numbers3h 57m

Introduction to Radical Expressions
47m

Simplifying Radical Expressions
47m

Adding and Subtracting Radicals
19m

Multiplying, Dividing, and Rationalizing Radicals
53m

Introduction to Complex Numbers
18m

Multiplying and Dividing Complex Numbers
51m

19. Quadratic Equations and Functions3h 1m

The Square Root Property
25m

Completing the Square
26m

The Quadratic Formula
40m

Graphing Quadratic Equations
1h 28m

20. Exponential and Logarithmic Functions2h 31m

Introduction to Inverse Functions
25m

Exponential Functions
35m

Introduction to Logarithmic Functions
33m

Properties of Logarithms
55m

21. Conic Sections and Systems of Nonlinear Equations2h 24m

Parabolas
35m

Graphing Circles
32m

Ellipses
35m

Hyperbolas
41m

22. Sequences, Series, and the Binomial Theorem1h 45m

Introduction to Sequences
40m

Arithmetic Sequences
27m

Geometric Sequences
26m

Factorials
11m

18. Roots, Radicals, and Complex Numbers

Multiplying and Dividing Complex Numbers

Prealgebra, Beginning Algebra, & Intermediate Algebra

18. Roots, Radicals, and Complex Numbers

Multiplying and Dividing Complex Numbers

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Multiple Choice

Find the quotient. Express your answer in standard form.
$\frac{- 5 + 3 i}{- 7 - 4 i}$

$$\frac$35+$\frac$45i$

$18i$

$23-41i$

$$\frac{23}{65}$-$\frac{41}{65}$i$

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Find the quotient. Express your answer in standard form.−5+3i−7−4i\(\frac{-5+3i}{-7-4i}\)

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Find the quotient. Express your answer in standard form.
$\frac{- 5 + 3 i}{- 7 - 4 i}$