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0. Fundamental Concepts of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

Pythagorean Theorem & Basics of Triangles
(0)

1. Equations and Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions & Graphs(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential and Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Measuring Angles(0)

Angles in Standard Position
(0)

Coterminal Angles
(0)

Complementary and Supplementary Angles
(0)

Radians
(0)

8. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
(0)

Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

9. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
(0)

Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

10. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

11. Inverse Trigonometric Functions and Basic Trig Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

12. Trigonometric Identities (0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

13. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

14. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

15. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

16. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

17. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

18. Systems of Equations and Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

19. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

20. Sequences, Series & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

21. Combinatorics and Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

22. Limits & Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

23. Intro to Derivatives & Area Under the Curve(0)

Tangent Lines & Derivatives
(0)

Limits at Infinity
(0)

Limits of Sequences
(0)

Area Under a Curve
(0)

1. Equations and Inequalities

The Imaginary Unit

1. Equations and Inequalities

The Imaginary Unit: Videos & Practice Problems

Video Lessons Practice Worksheet

20 problems

Problem 1Multiple Choice

Simplify the following expression and write the answer in standard form. (2√-7)(- 5√-18)

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Problem 2Multiple Choice

Simplify the following expression and write the answer in standard form: 7/(1 + 3/i)

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Problem 3Multiple Choice

Evaluate the following expression for x = 2i:

(x² + 12)/(3 - x)

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Problem 4Multiple Choice

Simplify the following expression and write the answer in standard form: (5 - i)² - (2 + 3i)²

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Problem 5Multiple Choice

Write the following expression in standard form: (3 + 2i)³

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Problem 6Multiple Choice

Write the following expression as -1, 1, -i, or i:

i⁸⁸

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Problem 7Multiple Choice

What is the imaginary unit 'i' defined as?

Problem 8Multiple Choice

How would you simplify the square root of -9 using the imaginary unit?

Problem 9Multiple Choice

Express the square root of -50 in terms of 'i'.

Problem 10Multiple Choice

Which of the following is the correct notation for expressing the solution to the square root of -72?

Problem 11Multiple Choice

Calculate the square root of -18 and express it in the correct form.

Problem 12Multiple Choice

Which of the following is an imaginary number?

Problem 13Multiple Choice

Evaluate and express the result of (3i) * (2i) in standard form.

Problem 14Multiple Choice

Identify the pattern in simplifying the square roots of -8, -18, and -32.

Problem 15Multiple Choice

What is the simplified form of √(-36)?

Problem 16Multiple Choice

Solve for the square root of -45 and express it in the correct form.

Problem 17Multiple Choice

If z = 3 + 4i, what is the result of z * z̅ (the conjugate of z)?

Problem 18Multiple Choice

Why was the imaginary unit 'i' created?

Problem 19Multiple Choice

What is the first step in simplifying √(-25) using the imaginary unit?

Problem 20Multiple Choice

Express √(-75) in terms of 'i'.

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Rational Equations Practice Problems Powers of i Practice Problems

Helpful Calculators for These Questions

Eigenvalue and Eigenvector Calculator

Calculate eigenvalues, eigenvectors, characteristic polynomials, and diagonalization with steps

Complex Numbers Calculator

Add, subtract, multiply, and divide complex numbers — with Argand diagrams and step-by-step solutions

Root Calculator (Square, Cube & Nth Roots)

Calculate and simplify square roots, cube roots, and any nth root — with prime factorization and step-by-step solutions

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