Math Problem Statement
(-7 + 3i)(-2 + 6i)
Solution
The problem shown in the image is:
To simplify this, we need to apply the distributive property (also known as the FOIL method for binomials). Here’s the process step by step:
Step 1: Distribute the terms
Step 2: Multiply the terms
Step 3: Simplify
Remember that . So:
Now, add all the terms:
Step 4: Combine like terms
Thus, the simplified answer is:
Would you like further details or explanations?
Here are 5 related questions you might consider:
- How do you multiply two complex numbers in general form?
- What is the significance of in complex number operations?
- How would the process differ if there were more than two complex numbers to multiply?
- What are some applications of complex numbers in real-life problems?
- How can you represent the result of this multiplication graphically on the complex plane?
Tip: Always remember that , and it plays a critical role when simplifying products involving complex numbers.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Algebraic Multiplication
Imaginary Numbers
Formulas
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
Theorems
Definition of Complex Multiplication
i^2 = -1
Suitable Grade Level
Grade 10-12 (High School)