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Questions and Answers
According to Euler's formula, $e^{i\pi} = -2$.
According to Euler's formula, $e^{i\pi} = -2$.
False (B)
Euler's formula states that $e^{ix} = cos(x) + i sin(x)$.
Euler's formula states that $e^{ix} = cos(x) + i sin(x)$.
True (A)
Euler's formula can be used to derive De Moivre's Theorem.
Euler's formula can be used to derive De Moivre's Theorem.
True (A)
The real part of $e^{ix}$ is $sin(x)$ according to Euler's Formula.
The real part of $e^{ix}$ is $sin(x)$ according to Euler's Formula.
Euler's formula holds true only for real values of $x$.
Euler's formula holds true only for real values of $x$.
If $e^{ix} = cos(x) + i sin(x)$, then $e^{-ix} = cos(x) - i sin(x)$.
If $e^{ix} = cos(x) + i sin(x)$, then $e^{-ix} = cos(x) - i sin(x)$.
Euler's formula is applicable in electrical engineering for AC circuit analysis.
Euler's formula is applicable in electrical engineering for AC circuit analysis.
Using Euler's formula, $cos(x)$ can be expressed as $\frac{e^{ix} - e^{-ix}}{2}$.
Using Euler's formula, $cos(x)$ can be expressed as $\frac{e^{ix} - e^{-ix}}{2}$.
Euler's formula provides a way to convert between polar and rectangular forms of complex numbers.
Euler's formula provides a way to convert between polar and rectangular forms of complex numbers.
The magnitude of $e^{ix}$, where x is any real number, is always equal to 2.
The magnitude of $e^{ix}$, where x is any real number, is always equal to 2.
Flashcards
Euler's Formula
Euler's Formula
Relates complex exponentials to trigonometric functions, stating e^(ix) = cos(x) + i*sin(x).
Study Notes
Euler's Formula
- e^(ix) = cos x + i sin x
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