To simplify the expression \((11 - i)(-2 + 3i)\), we'll use the distributive property (also known as FOIL in the case of binomials). Here's the step-by-step process:

\[
(11 - i)(-2 + 3i)
\]

1. Multiply the first terms:
\[
11 \times (-2) = -22
\]

2. Multiply the outer terms:
\[
11 \times 3i = 33i
\]

3. Multiply the inner terms:
\[
-i \times (-2) = 2i
\]

4. Multiply the last terms:
\[
-i \times 3i = -3i^2
\]

Since \(i^2 = -1\), we have:
\[
-3i^2 = -3(-1) = 3
\]

Now, add up all the terms:
\[
-22 + 33i + 2i + 3
\]

Combine like terms:
\[
(-22 + 3) + (33i + 2i) = -19 + 35i
\]

Thus, the simplified form of the expression is:
\[
-19 + 35i
\]

Would you like more details or further clarification?

### Related Questions:
1. How do you multiply two complex numbers in polar form?
2. What is the significance of the imaginary unit \(i\) in complex numbers?
3. Can you convert \(-19 + 35i\) to polar form?
4. How do you add or subtract complex numbers?
5. What are the applications of complex numbers in real-world problems?

### Tip:
When multiplying complex numbers, always remember that \(i^2 = -1\), which helps simplify terms involving powers of \(i\).

Learn how to simplify the complex number expression (11−i)(−2+3i) using the distributive property and properties of the imaginary unit. This solution includes a step-by-step breakdown, combining like terms and simplifying with i^2 = -1. Ideal for students in Grades 9-12.

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