1. **Problem statement:** Given the points $K(0,1,4)$, $K(8,7,7)$, and $K(4,3,3)$ labeled as $C$, $B$, and $A$ respectively, and the equation $z = 3 + 2i$ with real numbers $p$ and $q$, find the values of $p$ and $q$. 2. **Understanding the problem:** The problem involves complex numbers and points in 3D space. The equation $z = 3 + 2i$ suggests $z$ is a complex number with real part 3 and imaginary part 2. 3. **Given conditions:** The problem states $z=0$ and asks about $p$ and $q$ such that $z = p + qi$ equals $3 + 2i$ or other values. 4. **Analyzing the options:** The options given are: - $q = 13$, $p = -6$ - $9 = -13$, $p = -6$ - $q$, $p$ are real numbers with $p = 6$ 5. **Solution:** Since $z = 3 + 2i$, comparing with $z = p + qi$, we have: $$p = 3, \quad q = 2$$ 6. **Final answer:** $p = 3$, $q = 2$. Note: The problem's text is somewhat unclear, but based on the standard form of complex numbers, this is the consistent solution.