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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)

17. Graphing Complex Numbers

Products and Quotients of Complex Numbers

17. Graphing Complex Numbers

Products and Quotients of Complex Numbers: Videos & Practice Problems

Video Lessons Practice Worksheet

Products and Quotients of Complex Numbers Practice Problems

20 problems

Problem 1Multiple Choice

Multiply the following complex numbers and express the final answer in polar form.

z₁ = 9(cos 35° + i sin 35°)

z₂ = 7(cos 65° + i sin 65°)

views

Problem 2Multiple Choice

Multiply the following complex numbers and express the final answer in polar form.

z₁ = cos(π/5) + i sin(π/5)

z₂ = cos(π/2) + i sin(π/2)

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Problem 3Multiple Choice

Divide the following complex numbers (z₁/z₂) and express the final answer in polar form.

z₁ = 9[cos(5π/6) + i sin(5π/6)]

z₂ = 45[cos(π/6) + i sin(π/6)]

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Problem 4Multiple Choice

Divide the following complex numbers (z₁/z₂) and express the final answer in polar form.

z₁ = 14(cos 65° + i sin 65°)

z₂ = 7(cos 35° + i sin 35°)

Problem 5Multiple Choice

Given two complex numbers in polar form: z1 = 4 cis 30° and z2 = 3 cis 45°, what is the product z1 * z2?

Problem 6Multiple Choice

Which of the following is the correct cis notation for the complex number 5(cos 60° + i sin 60°)?

Problem 7Multiple Choice

Calculate the product of z1 = 2 cis 120° and z2 = 3 cis 150°.

Problem 8Multiple Choice

Simplify the expression 4 cis (π/4 + π/6) by finding a common denominator.

Problem 9Multiple Choice

What is the quotient of z1 = 8 cis 210° and z2 = 2 cis 150°?

Problem 10Multiple Choice

Which of the following represents the division of 10 cis 90° by 2 cis 30°?

Problem 11Multiple Choice

Find the quotient of z1 = 6 cis 135° and z2 = 3 cis 45°.

Problem 12Multiple Choice

Simplify the expression 5 cis (2π/3 - π/4) by finding a common denominator.

Problem 13Multiple Choice

Why is cis notation beneficial when working with complex numbers in polar form?

Problem 14Multiple Choice

What is the relationship between multiplication and division of complex numbers in polar form?

Problem 15Multiple Choice

If z1 = 7 cis 60° and z2 = 2 cis 120°, what is the product z1 * z2?

Problem 16Multiple Choice

Convert the expression 3(cos 45° + i sin 45°) into cis notation.

Problem 17Multiple Choice

Calculate the product of z1 = 5 cis 45° and z2 = 4 cis 135°.

Problem 18Multiple Choice

Simplify the expression 6 cis (π/2 + π/3) by finding a common denominator.

Problem 19Multiple Choice

What is the quotient of z1 = 9 cis 270° and z2 = 3 cis 90°?

Problem 20Multiple Choice

Which of the following represents the division of 12 cis 180° by 4 cis 60°?

Polar Form of Complex Numbers Practice Problems Powers of Complex Numbers (DeMoivre's Theorem) Practice Problems

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