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Last updated on May 26th, 2025

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Square Root of -484

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If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in various fields such as engineering, physics, and mathematics. Here, we will discuss the square root of -484.

Square Root of -484 for UAE Students
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What is the Square Root of -484?

The square root is the inverse of squaring a number. When dealing with negative numbers, the square root becomes more complex because no real number squared will result in a negative number. Thus, the square root of -484 is expressed in imaginary terms as it involves the imaginary unit 'i'. The square root of -484 can be expressed as √(-484) = √(484) × √(-1) = 22i, where 'i' is the imaginary unit defined as √(-1).

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Understanding the Square Root of Negative Numbers

For negative numbers, the square root is not defined within the set of real numbers. Instead, it's expressed using imaginary numbers. An imaginary number is a multiple of 'i', the square root of -1. Therefore, the square root of any negative number, such as -484, will involve 'i', making it an imaginary number. The expression becomes √(-484) = 22i, showing the multiplication of the real square root of 484 and the imaginary unit.

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Imaginary Unit and Its Properties

The imaginary unit 'i' is defined as the square root of -1. It is a fundamental part of complex numbers and is used when dealing with square roots of negative numbers. The key properties of 'i' include: 1. i² = -1 2. i³ = -i 3. i⁴ = 1 By understanding these properties, we can handle operations involving imaginary numbers more effectively, such as calculating powers or simplifying expressions involving 'i'.

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Applications of Imaginary Numbers

Imaginary numbers, including those derived from square roots of negative numbers, are crucial in various fields:

 

  • Electrical Engineering: Used in analyzing AC circuits.
  • Quantum Physics: Appear in wave functions and quantum mechanics.
  • Control Theory: Used in system stability analysis.
  • Signal Processing: Applied in Fourier transforms and signal analysis.

 

These applications highlight the importance of imaginary numbers in both theoretical and practical scenarios.

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Visualizing Complex Numbers

Complex numbers, which include real and imaginary parts, can be visualized on a complex plane. The horizontal axis represents the real part, while the vertical axis represents the imaginary part. For example, the complex number 22i is represented as a point on the vertical axis, 22 units above the origin. This visualization helps in understanding the operations and relationships between complex numbers.

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Common Mistakes and How to Avoid Them in the Square Root of -484

Students often make mistakes when dealing with square roots of negative numbers, such as ignoring the imaginary unit or not applying the properties of 'i' correctly. Let's review some common errors.

Mistake 1

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Forgetting the Imaginary Unit

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When finding the square root of a negative number, it is crucial to include the imaginary unit 'i'. Neglecting to do so leads to incorrect results.

 

For example, √(-484) should be correctly written as 22i, not just 22.

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Square Root of -484 Examples

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Problem 1

Can you help Max find the magnitude of the complex number 22i?

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The magnitude of the complex number 22i is 22.

Explanation

The magnitude of a complex number a + bi is given by √(a² + b²).

For 22i, a = 0 and b = 22.

Thus, the magnitude is √(0² + 22²) = √484 = 22.

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Problem 2

If a complex number is 22i, what is its conjugate?

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The conjugate of the complex number 22i is -22i.

Explanation

The conjugate of a complex number a + bi is a - bi.

For 22i, where a = 0 and b = 22, the conjugate is 0 - 22i, which is -22i.

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Problem 3

Calculate the result of (22i)².

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The result of (22i)² is -484.

Explanation

Using the property i² = -1, we have (22i)² = 22² × i² = 484 × -1 = -484.

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Problem 4

What is the real part of the complex number 7 + 22i?

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The real part is 7.

Explanation

A complex number is expressed as a + bi, where a is the real part. In 7 + 22i, the real part is 7.

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Problem 5

Find the imaginary part of the complex number -5 + 22i.

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The imaginary part is 22.

Explanation

In a complex number a + bi, b is the imaginary part. For -5 + 22i, the imaginary part is 22.

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FAQ on Square Root of -484

1.What is √(-484) in terms of i?

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2.What is an imaginary number?

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3.Why can't we find the square root of a negative number in real numbers?

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4.What is the meaning of the complex plane?

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5.How do you find the magnitude of a complex number?

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6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?

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7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square Root of -484?

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8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square Root of -484?

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9.Does learning Algebra support future career opportunities for students in United Arab Emirates?

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Important Glossary Terms for the Square Root of -484

  • Imaginary Number: A number that can be expressed in the form of a real number multiplied by the imaginary unit 'i', where i = √(-1).

 

  • Complex Number: A number comprising a real and an imaginary part, expressed as a + bi.

 

  • Imaginary Unit: Represented by 'i', it is the square root of -1, fundamental in defining complex numbers.

 

  • Magnitude: The length or size of a complex number, calculated as √(a² + b²) for a complex number a + bi.

 

  • Complex Plane: A visual representation of complex numbers with a horizontal axis for real parts and a vertical axis for imaginary parts.
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About BrightChamps in United Arab Emirates

At BrightChamps, we know algebra is more than symbols—it opens doors to endless possibilities! We’re dedicated to helping kids throughout the UAE develop crucial math skills, focusing today on the Square Root of -484 with a special focus on square roots—in an enjoyable, engaging, and easy-to-understand way. Whether your child is figuring out the speed of a roller coaster at Dubai Parks and Resorts, keeping track of local football scores, or budgeting their allowance for the latest gadgets, mastering algebra gives them confidence for everyday situations. Our interactive lessons make learning both fun and simple. Because kids in the UAE learn in varied ways, we customize our teaching to fit each child’s needs. From Dubai’s soaring skyscrapers to Abu Dhabi’s cultural heritage, BrightChamps brings math alive, making it relevant and exciting throughout the UAE. Let’s make square roots a joyful part of every child’s math journey!
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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