To expand $(i - 7)(i - 2)$, we use the distributive property (or FOIL method):

$(i - 7)(i - 2) = i \cdot i + i \cdot (-2) - 7 \cdot i - 7 \cdot (-2)$

Now, we calculate each term:

1. $i \cdot i = i^2$
2. $i \cdot (-2) = -2i$
3. $-7 \cdot i = -7i$
4. $-7 \cdot (-2) = 14$

So, we get:

$i^2 - 2i - 7i + 14$

Combine like terms:

$i^2 - 9i + 14$

Now, we know that $i^2 = -1$, so we substitute:

$-1 - 9i + 14$

Finally, combine constants:

$= 13 - 9i$

Thus, the result is:

$\boxed{13 - 9i}$

Would you like a deeper explanation of any steps?

Here are five questions to deepen understanding:

1. How do we apply the distributive property to binomials?
2. Why does $i^2$ equal $-1$?
3. Can we generalize the method used here for any two complex numbers?
4. How does the FOIL method help simplify complex expressions?
5. What are other ways to simplify complex number expressions?

Tip: Remember that $i^2 = -1$ is fundamental in complex number calculations.