Question

Perform the indicated operation & simplify. Express the answer in terms of i (as a complex number).
(12-9i)(10-6i)=

Answer 1

To perform the operation \((12 - 9i)(10 - 6i)\), we can use the distributive property (also known as the FOIL method for binomials).

1. Multiply the first terms:
\[
12 \cdot 10 = 120
\]

2. Multiply the outer terms:
\[
12 \cdot (-6i) = -72i
\]

3. Multiply the inner terms:
\[
-9i \cdot 10 = -90i
\]

4. Multiply the last terms:
\[
-9i \cdot (-6i) = 54i^2
\]
Since \(i^2 = -1\), we can replace \(54i^2\) with \(54(-1) = -54\).

Now, combine all the results:
\[
120 - 72i - 90i - 54
\]

Combine the real parts and the imaginary parts:
- Real part: \(120 - 54 = 66\)
- Imaginary part: \(-72i - 90i = -162i\)

Putting it all together, we get:
\[
66 - 162i
\]

Therefore, the final simplified result is:
\[
\boxed{66 - 162i}
\]