# Find Absolute Values Of Complex Numbers Worksheet

## 6 problems

To find the absolute value of a complex number $$a + bi$$, calculate the distance from the origin to the point $$(a, b)$$ in the complex plane. This is done using the formula $$\sqrt{a^2 + b^2}$$. The absolute value represents the magnitude of the complex number. We can use absolute values of a complex numbers calculator to easily compute this value.

Algebra 2
Real And Complex Numbers

## How Will This Worksheet on "Find Absolute Values of Complex Numbers" Benefit Your Student's Learning?

• Helps visualize the position of complex numbers in the complex plane.
• Demonstrates the magnitude of complex numbers in math and physics.
• Assists in calculating roots and powers of complex numbers, essential for solving math problems.
• Important in advanced math for analyzing functions, residues, and integrals.

## How to Find Absolute Values of Complex Numbers?

• A complex number is in the form $$a + bi$$, where $$a$$ is the real part and $$b$$ is the imaginary part.
• To find the absolute value $$|a + bi|$$, use the formula $$\sqrt{a^2 + b^2}$$.
• Square the real part $$a$$ and the imaginary part $$b$$, then add these squares together.
• Finally, take the square root of the sum to determine the absolute value of the complex number.

## Solved Example

Q. Find the absolute value.$\newline$$|-9i|$
Solution:
1. Absolute Value Calculation: What is the absolute value of $a + bi$? $\newline$$|a + bi| = \sqrt{a^2 + b^2}$
2. Expression Substitution: For $|-9i|$, $a = 0$ and $b = -9$$\newline$Use $|a + bi| = \sqrt{a^2 + b^2}$ and substitute the values.$\newline$ $|-9i| = \sqrt{0^2 + (-9)^2}$
3. Expression Simplification: Simplify $0^2 + (-9)^2$.$\newline$ $0^2 + (-9)^2$ $= 0 \times 0 + (-9\times (-9)$ $\newline$$= 0 + 81$ $= 81$
4. Final Value Calculation: Simplify $\sqrt{81}$ to find the value of $|-9i|$. $|-9i| = \sqrt{81} = \sqrt{9^2} = 9$

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