Perform the indicated operation \& simplify. Express the answer as a complex number. $$ (10-9 i)(3+4 i)=\square $$

Question

UpStudy AI · Accepted Answer

To perform the multiplication and simplify the expression $$ (10 - 9i)(3 + 4i) $$, follow these steps:

1. **Apply the Distributive Property:**

$$
(10 - 9i)(3 + 4i) = 10 \cdot 3 + 10 \cdot 4i - 9i \cdot 3 - 9i \cdot 4i
$$

2. **Multiply the Terms:**

$$
= 30 + 40i - 27i - 36i^2
$$

3. **Simplify Using $$ i^2 = -1 $$:**

$$
= 30 + (40i - 27i) - 36(-1)
$$
$$
= 30 + 13i + 36
$$

4. **Combine Like Terms:**

$$
= 66 + 13i
$$

**Final Answer:**

$$
66 + 13i
$$
$$ 66 + 13i $$

Perform the indicated operation & simplify. Express the answer as
a complex number.