Math Problem Statement
Dame la respuesta correcta
Solution
The expression given is . To solve this, we use Euler's formula:
Substituting , we get:
Now calculate the values of cosine and sine at :
Thus:
The correct answer is , which corresponds to option b.
Would you like further details on this, or do you have any questions?
Here are 5 related questions for deeper understanding:
- How is Euler's formula applied in other complex exponentials?
- What is the geometric interpretation of on the complex plane?
- How does the unit circle relate to sine and cosine values for different angles?
- Can you derive the values of and using Euler's formula?
- What are the properties of the imaginary unit ?
Tip: Familiarize yourself with common angles like , and on the unit circle to quickly solve problems involving Euler's formula.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Euler's Formula
Trigonometry
Formulas
Euler's Formula: e^(ix) = cos(x) + i sin(x)
Theorems
Euler's Formula
Suitable Grade Level
Grades 10-12
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