Où j'apprends que la formule d'Euler, familière aux ingénieur.es et physicienn.es pour son usage en physique ondulatoire, n'a été acceptée que 50 ans après son introduction et qu'elle est issue du problème de logarithme de nombres négatifs, tel log(-1), débattu par Leibniz et Jacques Bernouilli en 1712
https://www.youtube.com/watch?v=f8CXG7dS-D0
#complexAnalysis #maths #physics #engineering #complexNumber
Sometimes, you write a function to compute some complicated thing that has as yet no appearance to you at break-finger pace just to see what the thing looks like. Then, boom. You're looking at God's t-shirts. And it's cool.
#SabineHossenfelder - Do #ComplexNumbers Exist?
"Do complex #Numbers exist or are they just a convenient, #MathematicalTool that we use in science? With the exception of #QuantumMechanics, it is easy to get rid of complex numbers. But can you do quantum mechanics without complex numbers? A recent paper says no, you can't."
https://www.youtube.com/watch?v=ALc8CBYOfkw&ab_channel=SabineHossenfelder
#Math #Maths #Mathematics #Science #Physics #Equations #ComplexPlane #TheComplexPlane #ComplexNumber #e #i #Pi #QM #QuantumPhysics
Is the order of the #imaginaryNumber in a #complexNumber just a matter of preference? #math #maths #mathematics
(w+ix)+j(y+iz) = w+ix+jy−kz
(w+xi)+(y+zi)j = w+xi+yj+zk
Either it matters or −kz = zk. Wouldn't the same be true for i & j? So those #quaternions still aren't equal?
That would mean (a+ib)* = (a+bi). And so |a+ib|² = (a+ib)(a+bi)= a²+ibbi+abi+iba = a²+b²-aib+iba, given -ib=bi.
Consistency would prevent you noticing i doesn't commute with reals, either.
That's... disturbing.
