Math Problem Statement
Multiply and simplify the following complex numbers:
[(\pink{2-2i}) \cdot (\blue{4-4i})]
Solution
To multiply and simplify the complex numbers , we'll use the distributive property (FOIL method).
Let's go through the steps:
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First: Multiply the first terms from each binomial:
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Outer: Multiply the outer terms:
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Inner: Multiply the inner terms:
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Last: Multiply the last terms:
Recall that , so:
Now, add up all the terms:
Combine the real and imaginary parts:
Thus, the simplified result of multiplying is:
Would you like to see further details or have any questions?
Here are 5 related questions:
- What happens when you square a complex number?
- How do you divide complex numbers?
- How do you determine if two complex numbers are equal?
- What are the real and imaginary parts of a complex number?
- How do you graph a complex number on the complex plane?
Tip: When multiplying complex numbers, always simplify to to get the correct real and imaginary components.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Multiplication of Complex Numbers
Imaginary Unit
Formulas
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Theorems
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Suitable Grade Level
Grades 11-12