The problem is asking you to multiply two complex numbers: $(7 + 5i)$ and $(8 - 9i)$, and express the result in the form $a + bi$.

Let's go through the steps:

1. Multiply the two binomials using the distributive property (FOIL method): $(7 + 5i)(8 - 9i)$ Applying the FOIL method:

   • First: $7 \times 8 = 56$
   • Outer: $7 \times (-9i) = -63i$
   • Inner: $5i \times 8 = 40i$
   • Last: $5i \times (-9i) = -45i^2$

2. Simplify the expression: $56 - 63i + 40i - 45i^2$ Recall that $i^2 = -1$, so: $-45i^2 = -45(-1) = 45$

3. Combine like terms: $56 + 45 - 63i + 40i = 101 - 23i$

So, the simplified answer is: $101 - 23i$

Would you like more details or have any other questions?

Here are 5 related questions to deepen your understanding:

1. How do you multiply two complex numbers in general form?
2. Why is $i^2 = -1$ significant in complex number multiplication?
3. Can complex numbers be divided using a similar method?
4. What is the geometric interpretation of multiplying complex numbers?
5. How does the result of multiplying two complex numbers compare to just adding them?

Tip: Always remember to simplify any $i^2$ terms in complex number multiplication, since they turn into real numbers!