Periodic Complex exponential signal

[bibo_dvd]

hello guys ..
first of all , iam not sure that i should type this thread here . so excuse me for that

in this problem i can understand the part until it's said that w=0 then x(t)=1, which is periodic for any value of T
but i can't understand the part after that in the case of w is not equal to zero
so help me with this please :)
Thx guys

 

[DrClaude]

Perhaps Euler's formula will be of help:
$$
e^{i \omega_0 T} = \cos(\omega_0 T) + i \sin (\omega_0 T)
$$

 

[bibo_dvd]

okay , i know Euler's formula but i can't understand " wt=m*2*pi " or "T=m*(2pi/w) m=positive integer"

how did this part was given ??

 

[DrClaude]

You want ##
e^{i \omega_0 T} = \cos(\omega_0 T) + i \sin (\omega_0 T) = 1
##, meaning that ##\cos(\omega_0 T)=1## and ##\sin (\omega_0 T)=0##. What are the values of ##\omega_0 T## for which these equalities hold?

 

[bibo_dvd]

omg , now i understand , we need cos(wT) to be always 1 , so cos (2*pi) and (4*pi) and so on , yaaaayyyyy :D
Thx man for help :)