https://file.aiquickdraw.com/mathbot/file/1729088884201apnrkkhn.jpg

Let's work through the questions in the image:

1. **Vocabulary**: The imaginary unit \( i \) is defined as the square root of -1, that is, \( i = \sqrt{-1} \). It is used to express complex numbers, which consist of a real part and an imaginary part. For example, in a complex number like \( a + bi \), \( a \) is the real part and \( b \) is the imaginary part, with \( i \) indicating the imaginary component.

2. **Complete the sentence**: For the complex number \( 5 + 2i \), the imaginary part is **2** and the real part is **5**.

3. **Writing**: To add complex numbers, you simply add the real parts together and add the imaginary parts together separately. For example, when adding \( (a + bi) \) and \( (c + di) \), the result will be \( (a + c) + (b + d)i \).

4. **Which one doesn't belong?**: The number that does not belong with the others is \( \sqrt{3} + 6i \). This is because all the other numbers have either a purely real or purely imaginary part, whereas \( \sqrt{3} + 6i \) has both a non-zero real part (\( \sqrt{3} \)) and a non-zero imaginary part (\( 6i \)).

---

Do you need further explanation or clarification on any of these concepts? 

Here are 5 related questions to deepen your understanding:
1. What is the result of squaring the imaginary unit \( i \)?
2. How would you multiply two complex numbers like \( (3 + 4i) \) and \( (1 - 2i) \)?
3. Can a real number be considered a complex number? Why or why not?
4. How do you find the conjugate of a complex number like \( 5 + 2i \)?
5. What is the geometric interpretation of a complex number on the complex plane?

**Tip**: When working with complex numbers, always remember that \( i^2 = -1 \), which can simplify many calculations involving powers of \( i \).

What is the imaginary unit i defined as, and how can you use it? Complete the sentence for 5 + 2i, and identify the number that does not belong.

Learn how to define and use the imaginary unit i, identify the real and imaginary parts of a complex number like 5 + 2i, and determine which number doesn't belong in a set of complex numbers. Suitable for high school students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation