Table of contents

0. Review of College Algebra4h 43m
1. Measuring Angles40m
2. Trigonometric Functions on Right Triangles2h 5m
3. Unit Circle1h 19m
4. Graphing Trigonometric Functions1h 19m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
6. Trigonometric Identities and More Equations2h 34m
7. Non-Right Triangles1h 38m
8. Vectors2h 25m
9. Polar Equations2h 5m
10. Parametric Equations1h 6m
11. Graphing Complex Numbers1h 7m

11. Graphing Complex Numbers

Graphing Complex Numbers

Trigonometry

11. Graphing Complex Numbers

Graphing Complex Numbers

Previous problemNext problem

2:12 minutes

Problem 5

Textbook Question

In Exercises 1–8, add or subtract as indicated and write the result in standard form.6 − (−5 + 4i) − (−13 − i)

Verified step by step guidance

Step 1: Begin by distributing the negative sign across the terms inside the parentheses: \(6 - (-5 + 4i) - (-13 - i)\).

Step 2: Distribute the negative sign to the first set of parentheses: \(6 + 5 - 4i\).

Step 3: Distribute the negative sign to the second set of parentheses: \(6 + 5 - 4i + 13 + i\).

Step 4: Combine the real parts: \(6 + 5 + 13\).

Step 5: Combine the imaginary parts: \(-4i + i\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part and b is the coefficient of the imaginary unit i (where i is the square root of -1). Understanding how to manipulate complex numbers is essential for performing operations like addition and subtraction.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, combine their real parts and their imaginary parts separately. For example, when adding (a + bi) and (c + di), the result is (a + c) + (b + d)i. This concept is crucial for simplifying expressions involving complex numbers.

Standard Form of Complex Numbers

The standard form of a complex number is a + bi, where a and b are real numbers. When performing operations on complex numbers, it is important to express the final result in this form to clearly identify the real and imaginary components, facilitating further calculations or interpretations.