SIMPLIFY THE FOLLOWING (show complete solution): j1998+ j2005+ j100 1.

1. Graph the following complex numbers and convert in the specified form a. 5-j7 to exponential form b. 5 cjs (-45°) to rectangular form C. -2-j3 to polar form d. 32-45° to exponential form of complex numbers, (10pts each)

Q6. Figure Q6 shows a modulated waveform v(t) in microvolts as a function of time t in nanoseconds. 25 50 75 100 125 150 175 200 225 250 50 40 40 30 30 20 20 10 10 -10 -10 -20 -20 -30 -30 -40 -40 -50 -50 250 25 50 75 100 125 150 175 200 225 time/ns Figure Q6: Modulated waveform (a) Describe the modulation scheme. (b) What are the values of the carrier frequency and the modulation frequency? (c) What is the value of the modulation index? (d) What is the transmission efficiency (ratio of modulated to total power) in this example? (e) Sketch the spectrum of this modulated waveform indicating the relative magnitudes of the various spectral components. (f) The modulating wave in this example is substituted with a square wave of 50% duty cycle and of fundamental frequency 1.0 MHz. Sketch the absolute value of the spec- trum of the modulated waveform indicating the frequencies and relative magnitudes of the sideband components. (g) Demodulation of this type of signal is usually accomplished…

Reduce to its lowest form using sop