https://file.aiquickdraw.com/mathbot/file/1728037323025qf4vdlgg.jpg

Here are the solutions for the first set of problems from your image (complex number multiplication):

7) \( 8(-2i)(-5 - 4i) \)
   - Simplified: \( -16i(-5 - 4i) = -80i - 64 = -64 + 80i \)

8) \( (2 - 2i)^2 \)
   - This expression can be expanded to \( (2 - 2i)(2 - 2i) = 8i \)

9) \( (4i)(-2i)(-8 + 4i) \)
   - Simplified: \( (4i)(-2i)(-8 + 4i) = -64 + 32i \)

10) \( (-4 - 4i)(1 - 3i) \)
    - Expanding: \( (-4 - 4i)(1 - 3i) = -16 - 8i \)

11) \( (7 - 2i)(6 - 4i) \)
    - Simplified to: \( 50 - 34i \)

12) \( (4 - 3i)(6 - 6i) \)
    - Expanded: \( 42 - 18i \)

Would you like detailed steps for each? Let me know!

Here are some related questions you could explore:
1. What is the general process for multiplying complex numbers?
2. How can we simplify expressions with powers of \(i\)?
3. What are the steps to divide complex numbers?
4. How does multiplying conjugates simplify complex expressions?
5. How can we express a complex number in polar form?

**Tip:** Always simplify powers of \(i\) as \(i^2 = -1\).

Solve the complex number expressions provided in the image.

Explore how to solve complex number expressions involving multiplication and division. This guide covers key concepts such as multiplying complex numbers and using the conjugate method to divide complex expressions. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation