The complex number given is $9 + 8i$.

Step 1: Locate the Point on the Complex Plane

In this case:

• The real part ($\text{Re}$) is $9$.
• The imaginary part ($\text{Im}$) is $8$.

So, the point on the complex plane is $(9, 8)$.

Thus, the correct answer for the location of the point on the complex plane is:

• The complex plane is given. The horizontal axis is labeled "Re" and the vertical axis is labeled "Im". A point (9, 8) is graphed.

Step 2: Find the Modulus $r$

The modulus $r$ of a complex number $a + bi$ is given by the formula: $r = \sqrt{a^2 + b^2}$

For $9 + 8i$: $r = \sqrt{9^2 + 8^2} = \sqrt{81 + 64} = \sqrt{145}$

So, the modulus $r$ is: $r = \sqrt{145} \approx 12.04$

If you'd like more details or have any questions, feel free to ask!

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Here are some additional questions to deepen your understanding:

1. What is the argument (angle) of this complex number on the complex plane?
2. How do you graph complex numbers with negative imaginary parts?
3. How does the modulus change if the complex number is $-9 - 8i$?
4. What is the relationship between the modulus and distance from the origin?
5. How would the complex number look in polar form?

Tip: The modulus of a complex number tells you how far the point is from the origin on the complex plane.