Total energy possessed by a signal can be determined by integrating the square of the signal over its entire time duration. In this case, the signal is exp(jwt), where w represents the angular frequency and t represents time.

Calculating the energy of the signal follows these steps:

1. Define the signal: The given signal is exp(jwt), where exp is the exponential function, j is the imaginary unit (√(-1)), w is the angular frequency, and t is time.

2. Square the signal: To calculate the energy, we need to square the signal. When we square exp(jwt), we get exp(2jwt).

3. Integrate over the time duration: We integrate the squared signal over its entire time duration to calculate the energy. Since the time duration is not specified in the question, we assume it to be from -∞ to +∞ for simplicity.

4. Calculate the integral: The integral of exp(2jwt) over the entire time duration can be evaluated as:

∫[exp(2jwt)]dt = (1/2jw)[exp(2jwt)] + C

where C is the constant of integration.

5. Calculate the energy: To calculate the total energy, we evaluate the integral at the limits of -∞ and +∞:

Energy = lim[∫[exp(2jwt)]dt] as t approaches +∞ - lim[∫[exp(2jwt)]dt] as t approaches -∞

Since the exponential function exp(2jwt) is periodic with a period of 2pi/w, the limits of the integral will cancel out, and we are left with:

Energy = (1/2jw)[exp(2jwt)] from -∞ to +∞

6. Simplify the expression: Substituting the limits of the integral and simplifying, we get:

Energy = (1/2jw)[exp(2jw∞) - exp(2jw(-∞))]

Since exp(2jw∞) and exp(2jw(-∞)) are both undefined, the energy cannot be determined from this expression.

However, if we assume a finite time duration for the signal, such as from 0 to T, the energy can be calculated. In that case, the energy will be:

Energy = (1/2jw)[exp(2jwt)] from 0 to T

= (1/2jw)[exp(2jwT) - 1]

7. Simplify further: Substituting the limits of the integral and simplifying, we get:

Energy = (1/2jw)[exp(2jwT) - 1]

This expression represents the total energy possessed by the signal exp(jwt) over the time duration from 0 to T.

Based on the given options, the correct answer is option 'A', 2pi/w. However, it is important to note that the energy calculation assumes a finite time duration for the signal, which is not specified in the question.