[SOLVED] CPE381 Homework1

1.  Find and plot the roots of

z⁷ +1 = 0

2.  Represent the following complex numbers in alternative form (polar ßà {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 Euler’s identity to find trigonometric identities in terms of sin(α), sin(β), cos(α), and cos(β):
   1. sin(α + β)
   2. cos(α + β)

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 à           α =

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

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