Rewrite Expression Using Imaginary Number `I` Worksheet

Algebra 2
Real And Complex Numbers

Total questions - 6

Do you want to see how your students perform in this assignment?

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 ii to rewrite the expression below as a complex number.\newline95-\sqrt{-95}
Solution:
  1. Rewrite as product of square roots: Express 95- \sqrt{-95} as the product of square roots and 1\sqrt{-1}. 95- \sqrt{-95} = 195- \sqrt{-1 \cdot 95} = 195- \sqrt{-1} \cdot \sqrt{95}
  2. Express as complex number: Express 195- \sqrt{-1} \cdot \sqrt{95} as a complex number by using ii.
    - 95\sqrt{95}
    = - 195\sqrt{-1} \cdot \sqrt{95}
    = - i95i \cdot \sqrt{95}
    = - i95i \sqrt{95}
50,000+ teachers over use Byte!

Create your unique worksheets

  • star-iconAdd Differentiated practice to your worksheets
  • star-iconTrack your student’s performance
  • star-iconIdentify and fill knowledge gaps
Create your worksheet now

About Worksheet

Algebra 2
Real And Complex Numbers

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.

50,000+ teachers over the world use Byte!

Digitally assign and customise your worksheet using AI

  • star-iconAdd Differentiated practice to your worksheets
  • star-iconSee how your class performs
  • star-iconIdentify and fill knowledge gaps
Create your own assignment!

Class Performances tracking