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review derivation: Euler equation to e^(i pi) + 1 = 0

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
1 declare initial expr
  1. 4938429483; locally 1580045:
    \(\exp(i x) = \cos(x)+i \sin(x)\)
    \(e^{pdg_{1464} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{1464} \right)} + \cos{\left(pdg_{1464} \right)}\)
no validation is available for declarations 4938429483:
4938429483:
2 change variable X to Y
  1. 4938429483; locally 1580045:
    \(\exp(i x) = \cos(x)+i \sin(x)\)
    \(e^{pdg_{1464} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{1464} \right)} + \cos{\left(pdg_{1464} \right)}\)
  1. 3268645065:
    \(x\)
    \(pdg_{1464}\)
  2. 9350663581:
    \(\pi\)
    \(pdg_{3141}\)
  1. 8332931442; locally 1148677:
    \(\exp(i \pi) = \cos(\pi)+i \sin(\pi)\)
    \(e^{pdg_{3141} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{3141} \right)} + \cos{\left(pdg_{3141} \right)}\)
valid 4938429483:
8332931442:
4938429483:
8332931442:
3 simplify
  1. 8332931442; locally 1148677:
    \(\exp(i \pi) = \cos(\pi)+i \sin(\pi)\)
    \(e^{pdg_{3141} pdg_{4621}} = pdg_{4621} \sin{\left(pdg_{3141} \right)} + \cos{\left(pdg_{3141} \right)}\)
  1. 6885625907; locally 8524301:
    \(\exp(i \pi) = -1 + i 0\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
LHS diff is 0 RHS diff is pdg4621*sin(pdg3141) + cos(pdg3141) + 1 8332931442:
6885625907:
8332931442:
6885625907:
4 simplify
  1. 6885625907; locally 8524301:
    \(\exp(i \pi) = -1 + i 0\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
  1. 3331824625; locally 9610540:
    \(\exp(i \pi) = -1\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
valid 6885625907:
3331824625:
6885625907:
3331824625:
5 add X to both sides
  1. 3331824625; locally 9610540:
    \(\exp(i \pi) = -1\)
    \(e^{pdg_{3141} pdg_{4621}} = -1\)
  1. 4901237716:
    \(1\)
    \(1\)
  1. 2501591100; locally 9472905:
    \(\exp(i \pi) + 1 = 0\)
    \(e^{pdg_{3141} pdg_{4621}} + 1 = 0\)
valid 3331824625:
2501591100: error for dim with 2501591100
3331824625:
2501591100: N/A
6 declare final expr
  1. 2501591100; locally 9472905:
    \(\exp(i \pi) + 1 = 0\)
    \(e^{pdg_{3141} pdg_{4621}} + 1 = 0\)
no validation is available for declarations 2501591100: error for dim with 2501591100
2501591100: N/A
Physics Derivation Graph: Steps for Euler equation to e^(i pi) + 1 = 0

Symbols for this derivation

See also all 212 symbols
symbol ID category latex scope dimension name value Used in derivations references
1464 variable x
\(x\)
['real']
140
4621 variable i
\(i\)
['imaginary']
imaginary unit 74
3141 constant \pi
\(\pi\)
['real']
pi 3.1415   dimensionless
55
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