You can rewrite expressions involving negative roots by using \( i \).**Worked Example**You can use the number \( i \) to rewrite \( \sqrt{-25} \).1. Factor out \(-1\). \[ \sqrt{-25} = \sqrt{(-1)(25)} \]2. Rewrite the radical expression. \[ = \sqrt{-1} \cdot \sqrt{25} \]3. Apply the square root on \( \sqrt{25} \). \[ = 5\sqrt{-1} \]4. Rewrite \( \sqrt{-1} \) as \( i \). \[ = 5i \]So, \( \sqrt{-25} \) can be rewritten as \( 5i \).---**3. Rewrite each expression using \( i \).**a. \( \sqrt{-4} \)b. \( \sqrt{-12} \)c. \( 5 + \sqrt{-50} \)d. \( \frac{6 - \sqrt{-8}}{2} \) **Complex and Imaginary Numbers: Exercise****1. Complete each statement with *always*, *sometimes*, or *never*.**a. If a number is an imaginary number, then it is ______ a complex number.b. If a number is a complex number, then it is ______ an imaginary number.c. If a number is a real number, then it is ______ a complex number.d. If a number is a real number, then it is ______ an imaginary number.e. If a number is a complex number, then it is ______ a real number.---**2. Use the diagram on the previous page to list all number sets that describe each given number.**a. 3b. √7c. 3id. 5.45e. \( \frac{7}{8} \)f. 6 - i---*Note: The exercise prompts the student to analyze relationships between different sets of numbers, such as real, imaginary, and complex numbers. Students are also tasked with categorizing specific numbers into their relevant number sets.*

in multiple sub part , according to guideline we are allowed to answer only first three sub parts

Answered: 3. Rewrite each expression using i. a.…

Math

Algebra

3. Rewrite each expression using i. a. V-4 b. V-12 C. 5+V-50 6-V-8 d. 2

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

You can rewrite expressions involving negative roots by using \( i \).

**Worked Example**

You can use the number \( i \) to rewrite \( \sqrt{-25} \).

1. Factor out \(-1\).
\[
\sqrt{-25} = \sqrt{(-1)(25)}
\]

2. Rewrite the radical expression.
\[
= \sqrt{-1} \cdot \sqrt{25}
\]

3. Apply the square root on \( \sqrt{25} \).
\[
= 5\sqrt{-1}
\]

4. Rewrite \( \sqrt{-1} \) as \( i \).
\[
= 5i
\]

So, \( \sqrt{-25} \) can be rewritten as \( 5i \).

---

**3. Rewrite each expression using \( i \).**

a. \( \sqrt{-4} \)

b. \( \sqrt{-12} \)

c. \( 5 + \sqrt{-50} \)

d. \( \frac{6 - \sqrt{-8}}{2} \)

**Complex and Imaginary Numbers: Exercise**

**1. Complete each statement with *always*, *sometimes*, or *never*.**

a. If a number is an imaginary number, then it is ______ a complex number.

b. If a number is a complex number, then it is ______ an imaginary number.

c. If a number is a real number, then it is ______ a complex number.

d. If a number is a real number, then it is ______ an imaginary number.

e. If a number is a complex number, then it is ______ a real number.

---

**2. Use the diagram on the previous page to list all number sets that describe each given number.**

a. 3

b. √7

c. 3i

d. 5.45

e. \( \frac{7}{8} \)

f. 6 - i

---

*Note: The exercise prompts the student to analyze relationships between different sets of numbers, such as real, imaginary, and complex numbers. Students are also tasked with categorizing specific numbers into their relevant number sets.*

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