To solve the problem presented in the image:

Task 1: Graph the complex number $3 - i$

1. A complex number is expressed in the form $a + bi$, where $a$ is the real part and $b$ is the imaginary part.
   • Here, $a = 3$ (real part) and $b = -1$ (imaginary part).
2. On the graph:
   • The x-axis represents the real part.
   • The y-axis represents the imaginary part.
3. Plot the point at $(3, -1)$ on the complex plane. This is where $3$ (real) and $-1$ (imaginary) intersect.

Task 2: Find the absolute value of $3 - i$

The absolute value of a complex number $z = a + bi$ is calculated as: $|z| = \sqrt{a^2 + b^2}$ For $3 - i$: $|3 - i| = \sqrt{3^2 + (-1)^2} = \sqrt{9 + 1} = \sqrt{10}$

Final Answer:

1. The point $(3, -1)$ is graphed on the complex plane.
2. The absolute value is $\sqrt{10}$, approximately $3.16$.

Let me know if you'd like a deeper explanation or further examples!

Here are five related questions to expand on this:

1. How would you graph the complex number $-2 + 4i$ and find its absolute value?
2. What does the absolute value of a complex number represent geometrically?
3. How do you determine if two complex numbers are equal based on their graph?
4. Can you explain how complex numbers relate to polar coordinates?
5. What happens if the imaginary part of a complex number is zero?

Tip:

Always verify the coordinates on the graph to ensure accuracy when plotting complex numbers.