Simplify the expression to a + bi form:
left parenthesis, minus, 8, plus, 9, i, right parenthesis, left parenthesis, 12, plus, 10, i, right parenthesis
(−8+9i)(12+10i)

To simplify the expression \((−8+9i)(12+10i)\) into the form \(a + bi\), we will expand the product using the distributive property (FOIL method).

\[
(−8+9i)(12+10i)
\]

1. **First**: Multiply the first terms:
   \[
   (-8) \times 12 = -96
   \]

2. **Outer**: Multiply the outer terms:
   \[
   (-8) \times 10i = -80i
   \]

3. **Inner**: Multiply the inner terms:
   \[
   9i \times 12 = 108i
   \]

4. **Last**: Multiply the last terms:
   \[
   9i \times 10i = 90i^2
   \]

Since \(i^2 = -1\), the last term becomes:
\[
90i^2 = 90(-1) = -90
\]

Now, combine all these results:
\[
-96 - 80i + 108i - 90
\]

Next, combine the like terms:
- Combine the real parts: \(-96 - 90 = -186\)
- Combine the imaginary parts: \(-80i + 108i = 28i\)

Thus, the expression simplifies to:
\[
-186 + 28i
\]

So, the simplified form is \(-186 + 28i\).

Would you like more details or have any questions?

---

Here are 8 related questions:

1. How do you multiply complex numbers in general?
2. What is the significance of the imaginary unit \(i\)?
3. How can you find the modulus of a complex number?
4. How would you add or subtract complex numbers?
5. Can you explain the geometric interpretation of complex numbers?
6. How do you divide two complex numbers?
7. What is the polar form of a complex number?
8. How do complex conjugates help in simplifying complex expressions?

**Tip:** When multiplying complex numbers, always remember to use the distributive property and simplify using \(i^2 = -1\).

Learn how to simplify the expression (−8+9i)(12+10i) to the form a + bi using the distributive property and the definition of the imaginary unit. This problem involves multiplication of complex numbers and simplification of complex expressions, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation