[Solved] CPE381 Homework1

1. Find and plot the roots of

z⁷ +1 = 0

2. Represent the following complex numbers in alternative form (polar {Re,Im} z=x +jy ) a) 1 + j
   1. 1 j
   2. 5 e j210
   3. 5 e j210
   4. z z*
   5. if w = e^z and z=1+j find log(w)

3. Use Eulers identity to find trigonometric identities in terms of sin(), sin(), cos(), and cos():
   1. sin( + )
   2. cos( + )

4. Write a script in Matlab to plot cosine signal with frequency 2Hz and amplitude 4 damped with time constant of 1 second (e^-t ) for two seconds and sampling frequency of 20 Hz.

Plot the signal using plot and stem functions in Matlab.

Accelerometer with analog output, sensitivity 2g, and power supply of +3V is used in smartphone to determine orientation of the smartphone according to the figure below.

What are the values of X and Y components [in Volts] for the following positions

What is the angle of the smartphone if:

1. X = 1.875 V, Y = 0.8505 V =

2. X = 2.1495 V, Y = 1.875V =

Please draw a phone as a part of the solution to avoid confusion.