Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Understanding the Form of a Complex Number

Consider the complex number expressed as \( Y = 2 - 3i \). In this expression:

- **2** is the **real part** of the complex number.
- **-3i** is the **imaginary part** of the complex number, where \( i \) is the imaginary unit, representing the square root of -1.

#### Identifying Components:

- **Real Part**: The coefficient of the number without the imaginary unit \( i \). For \( Y = 2 - 3i \), the real part is **2**.
- **Imaginary Part**: The coefficient of the imaginary unit \( i \). For \( Y = 2 - 3i \), the imaginary part is **-3**.

If asked, "What is its sign?" the context is typically about the imaginary part unless otherwise specified. Here, the imaginary part is -3.

### Summary

Given a complex number \( Y = 2 - 3i \):
- The **real part** is **2**.
- The **imaginary part** is **-3**.

Understanding these components is crucial in performing operations with complex numbers, such as addition, subtraction, and multiplication.
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Transcribed Image Text:### Understanding the Form of a Complex Number Consider the complex number expressed as \( Y = 2 - 3i \). In this expression: - **2** is the **real part** of the complex number. - **-3i** is the **imaginary part** of the complex number, where \( i \) is the imaginary unit, representing the square root of -1. #### Identifying Components: - **Real Part**: The coefficient of the number without the imaginary unit \( i \). For \( Y = 2 - 3i \), the real part is **2**. - **Imaginary Part**: The coefficient of the imaginary unit \( i \). For \( Y = 2 - 3i \), the imaginary part is **-3**. If asked, "What is its sign?" the context is typically about the imaginary part unless otherwise specified. Here, the imaginary part is -3. ### Summary Given a complex number \( Y = 2 - 3i \): - The **real part** is **2**. - The **imaginary part** is **-3**. Understanding these components is crucial in performing operations with complex numbers, such as addition, subtraction, and multiplication.
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