find the product, $ab$, of the two complex numbers.

Explanation:

Step1: Identify complex numbers from the graph

From the complex plane, vector $A$ is at $(5, 0)$ and vector $B$ is at $(-3, 3)$. $$A = 5 + 0i = 5, \quad B = -3 + 3i$$

Step2: Set up the product expression

Multiply the two complex numbers using the distributive property. $$AB = 5 \cdot (-3 + 3i)$$

Step3: Distribute the real constant

Multiply each term inside the parentheses by 5. $$AB = 5(-3) + 5(3i) = -15 + 15i$$

Answer:

-15 + 15i