Introduction:
The given expression is exp(jwt), where exp represents the exponential function and j represents the imaginary unit. The variable w represents the angular frequency and t represents time. We are asked to find the fundamental period of this expression.

Definition of Fundamental Period:
The fundamental period of a periodic function is the smallest positive value of T for which the function repeats itself. In other words, if we shift the function by T, it will align perfectly with the original function.

Analysis:
To determine the fundamental period of exp(jwt), we need to find the value of T such that exp(jw(t+T)) = exp(jwt). Let's solve this equation.

Using Euler's Formula:
exp(jwt) can be rewritten using Euler's formula as cos(wt) + j*sin(wt). Therefore, we have:
cos(w(t+T)) + j*sin(w(t+T)) = cos(wt) + j*sin(wt)

Separating Real and Imaginary Parts:
Equating the real and imaginary parts of the above equation separately, we get:
cos(w(t+T)) = cos(wt)
sin(w(t+T)) = sin(wt)

Trigonometric Identities:
Using trigonometric identities, we can rewrite the above equations as:
cos(wt)*cos(wT) - sin(wt)*sin(wT) = cos(wt)
sin(wt)*cos(wT) + cos(wt)*sin(wT) = sin(wt)

Simplifying the Equations:
From the first equation, we can simplify as:
cos(wt)*(cos(wT) - 1) + sin(wt)*sin(wT) = 0
cos(wt)*[(cos(wT) - 1) + tan(wt)*sin(wT)] = 0

Since cos(wt) cannot be zero for all values of t, we must have:
cos(wT) - 1 + tan(wt)*sin(wT) = 0

Using Trigonometric Identity:
Using the trigonometric identity tan(x) = sin(x)/cos(x), we can rewrite the equation as:
cos(wT) - 1 + sin(wt)^2/cos(wt) = 0

Manipulating the Equation:
Multiplying through by cos(wt), we get:
cos(wT)*cos(wt) - cos(wt) + sin(wt)^2 = 0
cos(wT)*cos(wt) + sin(wt)^2 = cos(wt)

Using Trigonometric Identity:
Using the trigonometric identity cos^2(x) + sin^2(x) = 1, we can rewrite the equation as:
cos(wT)*cos(wt) + (1 - cos^2(wt)) = cos(wt)
cos(wT)*cos(wt) + 1 - cos^2(wt) = cos(wt)
cos(wT)*cos(wt) - cos^2(wt) = 0
cos(wt)*(cos(wT) - cos(wt)) = 0

Condition for Fundamental Period:
For the equation to be true for all values of t, we must have either cos(wt)