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

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2:16 minutes

Problem 7

Textbook Question

In Exercises 1–8, add or subtract as indicated and write the result in standard form.8i − (14 − 9i)

Verified step by step guidance

Identify the expression to simplify: \(8i - (14 - 9i)\).

Distribute the negative sign across the terms inside the parentheses: \(8i - 14 + 9i\).

Combine like terms by adding the imaginary parts: \(8i + 9i\).

Combine the real parts: \(-14\).

Write the result in standard form \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part.

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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, b is the imaginary part, and i is the imaginary unit defined as the square root of -1. Understanding complex numbers is essential for performing operations such as addition and subtraction.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, you 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. Writing complex numbers in this form helps in clearly identifying the real and imaginary components, which is important for further mathematical operations and interpretations.