Math Problem Statement
Multiply and simplify the following complex numbers: (2 + 5i) • (5 - 3i)
Solution
The problem shown is:
To multiply these complex numbers, we'll use the distributive property (FOIL method).
Step-by-step solution:
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Multiply the real and imaginary parts:
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Perform each multiplication:
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Simplify using :
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Combine all the terms: Simplifies to:
Final Answer:
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Related questions:
- What is the general form of a complex number?
- How do you divide complex numbers?
- How can you represent complex numbers geometrically?
- What is the conjugate of a complex number and how is it used?
- How do you find the magnitude of a complex number?
Tip:
When multiplying complex numbers, remember to simplify as to get a real number.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Algebra
Distributive Property
Formulas
(a + bi)(c + di) = (ac - bd) + (ad + bc)i
Theorems
Imaginary Unit Properties: i^2 = -1
Suitable Grade Level
Grades 10-12