How do you simplify the expression $$\frac{5+3i}{4-2i}$$ ?

Multiply the numerator and denominator by the conjugate of the denominator: $$\frac{(5+3i)(4+2i)}{(4-2i)(4+2i)} = \frac{20 + 10i + 12i - 6}{16 + 4} = \frac{14 + 22i}{20} = \frac{7 + 11i}{10}$$ .

How do you simplify $$\sqrt[4]{\frac{16a^4}{c^3}}$$ ?

Separate the fraction: $$\sqrt[4]{16} \cdot \sqrt[4]{a^4} \cdot \frac{1}{\sqrt[4]{c^3}} = 2 \cdot a \cdot \frac{1}{\sqrt[4]{c^3}} = \frac{2a}{\sqrt[4]{c^3}}$$ .

How do you factor $$\left(3x-4\right)^2+9\left(3x-4\right)+18$$ ?

Let $$u = 3x - 4$$ . Then the expression becomes $$u^2 + 9u + 18$$ . Factor to get $$(u + 3)(u + 6)$$ , substituting back gives $$(3x - 1)(3x + 2)$$ .

How do you factor $$2x^{\frac{1}{2}} + 3x^{\frac{1}{4}} - 2$$ ?

Factor out $$x^{\frac{1}{4}}$$ : $$x^{\frac{1}{4}}(2x^{\frac{1}{4}} + 3) - 2 = 0$$ . This leads to the factors $$\left(2x^{\frac{1}{4}} - 1\right)(x^{\frac{1}{4}} + 2)$$ .

What is the definition of a complex number?

A complex number is a number that can be expressed in the form $$a + bi$$ , where $$a$$ and $$b$$ are real numbers and $$i$$ is the imaginary unit, defined as $$\sqrt{-1}$$ .

What is the formula for the difference of squares?

The difference of squares formula states that $$a^2 - b^2 = (a - b)(a + b)$$ .

What is the square root of a variable raised to an exponent?

The square root of a variable raised to an exponent $$\sqrt{x^n}$$ is equal to $$x^{n/2}$$ .

How do you identify the roots of a quadratic equation?

The roots of a quadratic equation $$ax^2 + bx + c = 0$$ can be found using the quadratic formula: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

What is the process of rationalizing the denominator?

Rationalizing the denominator involves multiplying the numerator and denominator by a suitable expression to eliminate any radicals in the denominator.

What is the relationship between exponents and roots?

Exponents and roots are inversely related; for example, raising a number to a fractional exponent $$x^{\frac{m}{n}}$$ is equivalent to taking the nth root of $$x$$ raised to the mth power.

(AA) Unit 2 Midterm (2024) Flashcards

Student preview

14 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the process of simplifying a complex fraction?

Back

To simplify a complex fraction, multiply the numerator and the denominator by the least common denominator (LCD) of the fractions involved, then simplify the resulting expression.

2.

FLASHCARD QUESTION

Front

Back

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

13 questions

Understanding the Cell Cycle

Flashcard

•

10th Grade

11 questions

Review A2

Flashcard

•

10th Grade

11 questions

3D Design Vocabulary Flashcard

Flashcard

•

10th Grade

8 questions

CHILDREN 2 (1ST CLASS)

Flashcard

•

KG

12 questions

Organic 2 Exam 4 Review

Flashcard

•

KG

13 questions

Regular and Irregular Verbs

Flashcard

•

10th Grade

10 questions

Industrial Revolution and Marxism

Flashcard

•

10th Grade

9 questions

Medical Conditions and Symptoms

Flashcard

•

KG

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

20 questions

Figurative Language Review

Quiz

•

6th Grade

Discover more resources for Mathematics

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

13 questions

Model Exponential Growth and Decay Scenarios

Quiz

•

9th - 12th Grade

27 questions

7.2.3 Quadrilateral Properties

Quiz

•

9th - 12th Grade

16 questions

Converting Improper Fractions to Mixed Numbers

Quiz

•

4th - 10th Grade

10 questions

Simplifying Expressions by Combining Like Terms

Interactive video

•

6th - 10th Grade

10 questions

Simplifying Expressions with the Distributive Property

Interactive video

•

6th - 10th Grade

10 questions

Key Features of Quadratic Functions

Interactive video

•

8th - 12th Grade