# Rewrite Expression Using Imaginary Number I Worksheet

## 6 problems

To rewrite an expression using the imaginary number $$i$$, simply substitute $$i$$ wherever you encounter $$\sqrt{-1}$$ in the expression. For example, in rewrite expression using imaginary number $$i$$ worksheet, if you have $$\sqrt{-9}$$, replace it with $$3i$$ because $$\sqrt{-9} = \sqrt{9 \cdot (-1)} = 3i$$. This approach allows for handling calculations involving square roots of negative numbers using $$i$$, which is essential for solving equations and understanding complex numbers in various theoretical and practical contexts.

Algebra 2
Real And Complex Numbers

## How Will This Worksheet on "Rewrite Expression Using Imaginary Number i" Benefit Your Student's Learning?

• It helps students to understand complex numbers by using $$i$$ as the imaginary unit.
• Helps solve quadratic equations that have complex solutions involving $$i$$.
• Develops skills in solving problems with equations and expressions that include imaginary numbers.
• Improves skills in working with expressions that include $$i$$, making overall math abilities stronger.
• Encourages thinking deeply about how to use and interpret operations with complex numbers.

## How to Rewrite Expression Using Imaginary Number i?

• Identify any square roots of negative numbers in the expression.
• Replace $$\sqrt{-1}$$ with $$i$$, the imaginary unit.
• Calculate the value of each term involving $$i$$.
• Combine real and imaginary parts if necessary to simplify the expression.

## Solved Example

Q. Use the imaginary number $i$ to rewrite the expression below as a complex number.$\newline$$-\sqrt{-95}$
Solution:
1. Rewrite as product of square roots: Express $- \sqrt{-95}$ as the product of square roots and $\sqrt{-1}$. $- \sqrt{-95}$ = $- \sqrt{-1 \cdot 95}$ = $- \sqrt{-1} \cdot \sqrt{95}$
2. Express as complex number: Express $- \sqrt{-1} \cdot \sqrt{95}$ as a complex number by using $i$.
- $\sqrt{95}$
= - $\sqrt{-1} \cdot \sqrt{95}$
= - $i \cdot \sqrt{95}$
= - $i \sqrt{95}$

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