Find Complex Conjugate 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 "Find Complex Conjugate" Benefit Your Student's Learning?

  • Simplifies division and multiplication of complex numbers.
  • Helps rationalize denominators in complex fractions.
  • Enhances understanding of how complex numbers work.
  • Assists in solving equations with complex roots.
  • Useful for practical problems in physics, engineering, and math. 

How to Find Complex Conjugate?

  • Start with a complex number in the form \( a + bi \), where \( a \) is the real part and \( b \) is the imaginary part.
  • Keep the real part \( a \) the same and change the sign of the imaginary part \( b \).
  • Combine the unchanged real part with the new imaginary part to form \( a - bi \).

Solved Example

Q. Find the sum of 27i2 - 7i and its complex conjugate.\newlineWrite your answer in the form a+bia + bi.
Solution:
  1. Identify the real and imaginary parts:The coefficient of i is imaginary and the number without i is real.
    In 27i2 - 7i, 22 is the real part and 7-7 is the imaginary part.
  2. Identify Complex Conjugate: Reasoning: Identify the complex conjugate of 27i2 - 7i.
    Calculation: The complex conjugate of 27i2 - 7i is 2+7i2 + 7i.
  3. Add complex number and conjugate:Add the original complex number and its conjugate.
    Calculation: (27i)+(2+7i)=2+2+(7i+7i)=4+0i=4(2 - 7i) + (2 + 7i) = 2 + 2 + (-7i + 7i) = 4 + 0i = 4
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 find the complex conjugate of a complex number, just change the sign of the imaginary part. For example, the conjugate of \( a + bi \) is \( a - bi \). This helps simplify calculations with complex numbers. The formula is simple: if \( z = a + bi \), then the conjugate is \( \overline{z} = a - bi \). See complex conjugate examples for more details.
Example: Find the complex conjugate of \( 4 + 5i \).

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