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Question 1. Express each of the following complex numbers in Cartesian form ( x + jy):
a. (1/2)ejπ
b. √2 e(-jπ/4)
Question 2. Express each of the following complex numbers in polar form (reθ, with -π< θ ≤π):
a. 1 + j
b. j (1-j)
c. (1 + j ) / (1 - j)
d. -3 j
Question 3. Find the Amplitude, fundamental period, frequency and phase for the following sine wave
a. s1(t)=10sin?(2000πt+(π/3 ))
b. s2(t)=sin?(5πt-π)
Question 4. Plot the following signals
a. sin?(2πt),
b. sin?(2πt+(π/2 ))
c. sin?(2πt+π)
d. sin?(2πt+(3π/2 ))
Question 5. Plot the frequency component of signal
4 sin?(200πt+(π/3 ))+sin?(10πt-π)
What is the bandwidth of this signal?
Using the geometry of Fig, prove that the most efficient circular open channel (maximum hydraulic radius for a given flow area) is a semicircle.
Derive an expression for electron concentration in conduction band and hole concentration in valance band
If the temperatures of the inner and outer surfaces of the bottom of the pan are 104°C and 105°C, respectively, determine the rate of energy destruction within the bottom of the pan during this process, in W. Take T0 = 25°C.
A 10-V independent voltage source is in series with a 2-Aindependent current source. What single source is equivalent to this series combination? Give the type and value of the equivalent source.
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Problem 2. Sketch the following periodic wave-forms
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Write a report on environmental companies
The saturation flow rate of the approach is 1800 veh/h, the cycle length is 60 seconds, and the effective green time is 40 seconds. Determine the total vehicle delay until complete queue clearance.
Compute the stresses in laminate coordinates at top and bottom of each lamina in Example 6.1 (p. 178) when the laminate is subjected to ?0x = 765(10-6 ) mm/mm, ?0y = -280(10-6 ) mm/mm, κxy = 34.2(10-6 )1/mm and all remaining strains and curvatures ..
A steel rod is bent into a semicircular ring of radius 36 in. and is supported in part by cables BD and BE which are attached to the ring at B. Knowing that the tension in cable BD is 55 lb, determine the components of the force exerted by the cab..
A discrete-time system can be described in one of two ways. One is by the unit-pulse response of the system, and the other is by the difference equation. In the first case, if we are given an input and want to find the output, we have to convolv..
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