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Questions and Answers
Euler's formula relates which fundamental mathematical functions?
Euler's formula relates the trigonometric functions and the complex exponential function.
What is the complex exponential function sometimes denoted as?
The complex exponential function is sometimes denoted as $e^{ix} = \cos(x) + i\sin(x)$.
What is Euler's identity?
Euler's identity is $e^{i\pi} + 1 = 0$ or $e^{i\pi} = -1$.
According to Richard Feynman, what did he call Euler's formula?
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Who presented a geometrical argument in 1714 that can be interpreted as a precursor to Euler's formula?
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Study Notes
Euler's Formula
- Relates trigonometric functions (sine and cosine) to exponential functions (e)
Notations
- Complex exponential function is sometimes denoted as cis(x)
Euler's Identity
- Considered the most beautiful equation in mathematics
Quotes
- Richard Feynman referred to Euler's formula as "our jewel"
History
- In 1714, Roger Cotes presented a geometrical argument that can be seen as a precursor to Euler's formula
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Description
Test your understanding of Euler's formula with this quiz! Challenge yourself with questions about the relationship between trigonometric functions and complex exponential functions, named after mathematician Leonhard Euler.
