Complex exponentials obey the expected rules of algebra when doing integrals and derivatives. Consider the complex signal z(t) = Zejлt/2 where Z = e¯jπ/³¸ (a) Show that the first derivative of z(t) with respect to time can be represented as a new com- plex exponential Qejлt/², i.e., ¼z(t) = Qеjлt/2. Determine the value for the complex amplitude Q. How much greater (or smaller) is the angle of Q than the angle of Z. (b) Evaluate the definite integral of z(t) over the range 0 < t < 1: 1 z(t)dt = ? Note that integrating a complex quantity follows the expected rules of algebra: you could integrate the real and imaginary parts separately, but you can also use the integration formula for an exponential directly on z(t). (c) Evaluate the integral of the magnitude squared |z(t)|² over the range -1 ≤ t ≤ 1: 1 [ \z (1)³ dt = ? -1

! Required information x(t) A - The given figure is a graph of one fundamental period of a periodic function x(f). A CTFS harmonic function cx[k] is found based on the representation time being the same as the fundamental period To, where A1 = 5, A2 = -3, and To = 5. Determine the numerical value of cx[0]. The numerical value of cx[O] is

it says COSINE not sine  Is the signal x(t)=2+ sin 2 - 3 cosлt periodic? Can it be expressed using complex exponentials