# Find Complex Conjugate Worksheet

## 6 problems

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 $$4 + 5i$$.

Algebra 2
Real And Complex Numbers

## 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 $2 - 7i$ and its complex conjugate.$\newline$Write your answer in the form $a + bi$.
Solution:
1. Identify the real and imaginary parts:The coefficient of i is imaginary and the number without i is real.
In $2 - 7i$, $2$ is the real part and $-7$ is the imaginary part.
2. Identify Complex Conjugate: Reasoning: Identify the complex conjugate of $2 - 7i$.
Calculation: The complex conjugate of $2 - 7i$ is $2 + 7i$.
3. Add complex number and conjugate:Add the original complex number and its conjugate.
Calculation: $(2 - 7i) + (2 + 7i) = 2 + 2 + (-7i + 7i) = 4 + 0i = 4$

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