Euler's equation (complex analysis)
GPTKB entity
Statements (31)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Euler's_formula
|
| gptkbp:category |
gptkb:mathematics
mathematical constants |
| gptkbp:field |
gptkb:mathematics
complex analysis |
| gptkbp:hasApplication |
electrical engineering
partial differential equations wave mechanics rotations in the complex plane |
| gptkbp:hasSpecialCase |
gptkb:Euler's_identity
|
| https://www.w3.org/2000/01/rdf-schema#label |
Euler's equation (complex analysis)
|
| gptkbp:i |
square root of -1
|
| gptkbp:implies |
e^{i\\pi} + 1 = 0
|
| gptkbp:introduced |
gptkb:Leonhard_Euler
|
| gptkbp:introducedIn |
1748
|
| gptkbp:isFundamentalTo |
mathematical physics
complex exponentials harmonic motion phasor analysis |
| gptkbp:relatedTo |
trigonometric functions
exponential function imaginary unit |
| gptkbp:statedIn |
e^{ix} = \\cos x + i \\sin x
|
| gptkbp:usedIn |
gptkb:signal_processing
Fourier analysis quantum mechanics |
| gptkbp:variant |
x (real number)
i (imaginary unit) |
| gptkbp:bfsParent |
gptkb:Euler_equation
|
| gptkbp:bfsLayer |
6
|