The expression \(\left|-7-i\right|\) represents the **magnitude** or **absolute value** of the complex number \(-7 - i\).

The magnitude of a complex number \(a + bi\) is given by the formula:

\[
\left| a + bi \right| = \sqrt{a^2 + b^2}
\]

For \(-7 - i\):
- \(a = -7\)
- \(b = -1\)

Now applying the formula:

\[
\left| -7 - i \right| = \sqrt{(-7)^2 + (-1)^2} = \sqrt{49 + 1} = \sqrt{50} = 5\sqrt{2}
\]

Thus, \(\left|-7-i\right| = 5\sqrt{2}\).

Would you like any further clarification on this? Here are some related questions:

1. How do you find the magnitude of any complex number?
2. What is the geometric interpretation of the magnitude of a complex number?
3. How do you add or subtract two complex numbers?
4. What are the real and imaginary components of a complex number?
5. How can you represent complex numbers graphically on the complex plane?

**Tip**: The magnitude of a complex number can be thought of as its distance from the origin on the complex plane.

The query submitted by the user: |−7−i|

Explore how to find the magnitude of the complex number −7−i. This solution demonstrates the application of the formula |a + bi| = sqrt(a^2 + b^2) to solve for the magnitude, yielding the answer 5√2. Suitable for students in Grades 10-12.

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