The problem involves multiplying two complex numbers: $(2 + 7i)$ and $(5 - 9i)$. The goal is to simplify the expression in the form $a + bi$, where $a$ and $b$ are real numbers.

Let's solve it step-by-step using the distributive property (also known as FOIL method for binomials):

$(2 + 7i)(5 - 9i) = 2(5) + 2(-9i) + 7i(5) + 7i(-9i)$

1. $2(5) = 10$
2. $2(-9i) = -18i$
3. $7i(5) = 35i$
4. $7i(-9i) = -63i^2$

Since $i^2 = -1$, the last term becomes:

$-63i^2 = -63(-1) = 63$

Now, add all the terms together:

$10 + (-18i) + 35i + 63$

Combine like terms:

1. Real part: $10 + 63 = 73$
2. Imaginary part: $-18i + 35i = 17i$

So, the result is:

$73 + 17i$

Thus, the simplified answer is $73 + 17i$.

Would you like further details or have any questions? Here are five related questions:

1. How do you multiply complex numbers using the FOIL method?
2. Why does $i^2 = -1$?
3. Can you explain why the real and imaginary parts are combined separately?
4. How would you divide complex numbers?
5. What happens if both complex numbers have negative real parts?

Tip: Always remember to use $i^2 = -1$ when simplifying complex number multiplications!