# Find Complex Conjugate Then Apply Operations Worksheet

## 6 problems

To find the complex conjugate, change the sign of the imaginary part of the complex number. For example, the conjugate of $$3 + 4i$$ is $$3 - 4i$$. After finding the conjugate, we can apply operations like addition, subtraction, multiplication, or division to simplify expressions or solve equations. For detailed examples and steps, refer to the find complex conjugate then apply operations pdf.

Algebra 2
Real And Complex Numbers

## How Will This Worksheet on "Find Complex Conjugate then Apply Operations" Benefit Your Student's Learning?

• Simplifies multiplication and division of complex numbers by eliminating imaginary parts.
• Helps simplify complex fractions by removing imaginary terms.
• Improves algebra and calculus skills, especially for equations with complex solutions.
• Enhances understanding of the interaction between real and imaginary parts in complex numbers.
• Builds skills needed for complex analysis and advanced calculus topics.

## How to Find Complex Conjugate Then Apply Operations?

• Begin with a complex number $$a + bi$$, where $$a$$ is the real part and $$b$$ is the imaginary part.
• Change the sign of the imaginary part to obtain $$a - bi$$.
• Perform addition, subtraction, multiplication, or division using the complex conjugate.

## Solved Example

Q. Find the sum of $-8 + 7i$ and its complex conjugate.$\newline$Write your answer in the form $a+bi$.
Solution:
1. Identify complex conjugate: Identify the complex conjugate of $-8 + 7i$.$\newline$ Complex conjugate: $-8 - 7i$
2. Add original and conjugate: Add the original number and its complex conjugate.$\newline$ $-8 + 7i + (-8 - 7i)$
3. Combine like terms: Combine like terms.$\newline$ Real part: $-8 + (-8) = -16$$\newline$ Imaginary part: $7i - 7i = 0$
4. Sum of real and imaginary parts: Sum of the real and imaginary parts.$\newline$ $-16 + 0i = -16$

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”