Math Problem Statement
Multiply (10 - 3i)(5 + 2i).
Solution
The problem is asking you to multiply two complex numbers, .
Step-by-Step Solution:
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Use the distributive property (FOIL method) to multiply:
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Simplify each term:
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Combine like terms:
= 50 + 5i - 6i^2$$ -
Recall that :
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Simplify the expression further:
Final Answer:
The product is , so the correct option is the first one: .
Do you need further details on any of the steps? Here are some related questions:
- How do you multiply two complex numbers in general?
- What is the significance of in complex number multiplication?
- Can you explain the FOIL method in more detail?
- What happens when you multiply complex conjugates?
- How would you add or subtract complex numbers?
Tip: Always remember that when dealing with imaginary numbers.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Algebra
Distributive Property (FOIL Method)
Formulas
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
i^2 = -1
Theorems
Multiplication of Complex Numbers
Suitable Grade Level
Grades 9-11