solve all questions and write all your work please solve the 8 questions and show work and explanation please! 1. (5 Points) Express 2ej3/4 in Cartesian form x+jy : 2. (5 Points) Express (1+j3)/(1j) in polar form rej, with <. 3. (10 Points) Determine the values of E and P for the signal x(t)=e3tu(t). 4. (10 Points) Compute y[n]=x[n]h[n], where x[n]=(21)nu[n1] and h[n]=u[n+1]. 5. (10 Points) Compute y(t)=x(t)h(t), where x(t)=u(t1)u(t3) and h(t)=e3t. 6. (20 Points) Which of following impulse responses correspond(s) to stable LTI systems? Show why? a. h1(t)=e(1j)tu(t) b. h2[n]=2nu[n+2] 7. (20 Points) For the continuous-time periodic signal x(t)=1+2cos(3t)+4sin(32t), determine the fundamental frequency 0 and the Fourier series coefficients ak such that x(t)=k=akejk0t 8. (20 Points) Suppose we are given the following information about a signal x[n] : a. x[n] is a real and even signal. b. x[n] has a period N=8 and Fourier coefficients ak. c. a9=4. d. 81n=07x[n]2=32. Find numerical values for the constants A,B and C, where x[n]=cos(Bn+C). Write not only answers but also all your works for the following problems. 1. (5 Points) Express 2ej3/4 in Cartesian form x+jy : 2. (5 Points) Express (1+j3)/(1j) in polar form rej, with < 3. (10 Points) Determine the values of E and P for the signal x(t)=e3tu(t). 4. (10 Points) Compute y[n]=x[n]h[n], where x[n]=(21)nu[n1] and h[n]=u[n+1]. 5. (10 Points) Compute y(t)=x(t)h(t), where x(t)=u(t1)u(t3) and h(t)=e3t. 6. (20 Points) Which of following impulse responses correspond(s) to stable LTI systems? Show why? a. h1(t)=e(1j)tu(t) b. h2[n]=2nu[n+2] 7. (20 Points) For the continuous-time periodic signal x(t)=1+2cos(3t)+4sin(32t), determine the fundamental frequency 0 and the Fourier series coefficients ak such that x(t)=k=akejk0t 8. (20 Points) Suppose we are given the following information about a signal x[n] : a. x[n] is a real and even signal. b. x[n] has a period N=8 and Fourier coefficients ak. c. a9=4. d. 81n=07x[n]2=32 Find numerical values for the constants A,B and C, where x[n]=cos(Bn+C)..