A*exp(jwt)=A*cos(wt+phi)?

[Grhymn]

1. The problem statement, all variables and given/known data

proving that A*exp(jwt)=A*cos(wt+phi)

2. Relevant equations
exp(jwt)=cos(wt)+jsin(wt)


3. The attempt at a solution
A*exp(jwt)=A*(cos(wt)+jsin(wt)) = A*(cos(wt)+tan(phi)sin(wt)) with tan(phi)=j
=A/cos(phi)*(cos(phi)cos(wt)+sin(phi)sin(wt))

The problem is that arctan(j) doesn't exist

[kikushiyo]

Hello !

I think you miss some data, since your formula is not true in general... If A,w and t are real numbers, the right hand side is real but the left hand side is complex...