What Is The Sum Of $\sqrt{-2}$ And $\sqrt{-18}$?A. $4 \sqrt{2}$B. $4 I \sqrt{2}$C. $5 \sqrt{2}$D. $5 I \sqrt{2}$

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Introduction

In mathematics, the square root of a negative number is a complex number. It is denoted by the letter 'i' and is defined as the square root of -1. In this article, we will explore the sum of $\sqrt{-2}$ and $\sqrt{-18}$.

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit. The imaginary unit 'i' is defined as the square root of -1.

$\sqrt{-2}$ can be written as $\sqrt{-1} \times \sqrt{2}$, which is equal to $i\sqrt{2}$.

Similarly, $\sqrt{-18}$ can be written as $\sqrt{-1} \times \sqrt{18}$, which is equal to $i\sqrt{18}$.

Simplifying $\sqrt{18}$

$\sqrt{18}$ can be simplified as $\sqrt{9 \times 2}$, which is equal to $3\sqrt{2}$.

Therefore, $\sqrt{-18}$ can be written as $i \times 3\sqrt{2}$, which is equal to $3i\sqrt{2}$.

Finding the Sum

Now that we have simplified $\sqrt{-2}$ and $\sqrt{-18}$, we can find their sum.

The sum of $\sqrt{-2}$ and $\sqrt{-18}$ is equal to $i\sqrt{2} + 3i\sqrt{2}$.

Combining Like Terms

We can combine the like terms $i\sqrt{2}$ and $3i\sqrt{2}$ by adding their coefficients.

The sum of $i\sqrt{2}$ and $3i\sqrt{2}$ is equal to $4i\sqrt{2}$.

Conclusion

In conclusion, the sum of $\sqrt{-2}$ and $\sqrt{-18}$ is equal to $4i\sqrt{2}$.

Answer

The correct answer is B. $4i\sqrt{2}$.

Final Thoughts

In this article, we explored the sum of $\sqrt{-2}$ and $\sqrt{-18}$. We simplified the square roots and combined like terms to find the final answer. This article demonstrates the importance of understanding complex numbers and their properties.

References

• [1] "Complex Numbers" by Math Open Reference
• [2] "Square Root of a Negative Number" by Wolfram MathWorld

Additional Resources

• [1] "Complex Numbers" by Khan Academy
• [2] "Square Root of a Negative Number" by MIT OpenCourseWare
  Frequently Asked Questions (FAQs) About Complex Numbers =====================================================

Introduction

In our previous article, we explored the sum of $\sqrt{-2}$ and $\sqrt{-18}$. In this article, we will answer some frequently asked questions about complex numbers.

Q: What is a complex number?

A: A complex number is a number that can be expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit.

Q: What is the imaginary unit 'i'?

A: The imaginary unit 'i' is defined as the square root of -1. It is used to extend the real number system to the complex number system.

Q: How do I simplify a complex number?

A: To simplify a complex number, you can use the following steps:

1. Simplify the real part of the complex number.
2. Simplify the imaginary part of the complex number.
3. Combine the simplified real and imaginary parts.

Q: What is the conjugate of a complex number?

A: The conjugate of a complex number is obtained by changing the sign of the imaginary part. For example, the conjugate of 3 + 4i is 3 - 4i.

Q: How do I add complex numbers?

A: To add complex numbers, you can use the following steps:

1. Add the real parts of the complex numbers.
2. Add the imaginary parts of the complex numbers.
3. Combine the simplified real and imaginary parts.

Q: How do I multiply complex numbers?

A: To multiply complex numbers, you can use the following steps:

1. Multiply the real parts of the complex numbers.
2. Multiply the imaginary parts of the complex numbers.
3. Combine the simplified real and imaginary parts.

Q: What is the modulus of a complex number?

A: The modulus of a complex number is the distance from the origin to the point representing the complex number in the complex plane.

Q: How do I find the modulus of a complex number?

A: To find the modulus of a complex number, you can use the following formula:

|z| = √(a^2 + b^2)

where z = a + bi is the complex number.

Q: What is the argument of a complex number?

A: The argument of a complex number is the angle between the positive real axis and the line segment representing the complex number in the complex plane.

Q: How do I find the argument of a complex number?

A: To find the argument of a complex number, you can use the following formula:

arg(z) = arctan(b/a)

where z = a + bi is the complex number.

Conclusion

In this article, we answered some frequently asked questions about complex numbers. We hope that this article has provided you with a better understanding of complex numbers and their properties.

References

• [1] "Complex Numbers" by Math Open Reference
• [2] "Square Root of a Negative Number" by Wolfram MathWorld

Additional Resources

• [1] "Complex Numbers" by Khan Academy
• [2] "Square Root of a Negative Number" by MIT OpenCourseWare