Compute the absolute value and argument of e^(log 2)(1+j) and plot the same.

Compute the absolute value and argument of e^(log 2)(1+j) and plot the same.
Problem 1
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Plot real part, imaginary part and absolute value of for -2st3 2. You can use MATLAB to plot the functions but show your derivations and justify your plot.
Determine the value of sup1≤X≤2 log (E [X]) - E [log (X)], that is, of all random variables X taking values between 1 and 2, find the largest value of log (E [X]) - E [log (X)]. Also interpret what this question is asking.
Determine the value of sup1≤X≤2 log (E [X]) - E [log (X)], that is, of all random variables X taking values between 1 and 2, find the largest value of log (E [X]) - E [log (X)]. Also interpret what this question is asking.
Compute the Discrete-Time Fourier Transform analytically for the following signals and plot the absolute values and the phase of the DTFT from-2π to 2π x[n] αηυ[n] for α-0.7 and 0.3 x[n]-δ[n-r] for τ-2 and 3 xInrk], for r -2 and 3 a. b. C. Please show your work step by step and include the formula for finding the absolute value of DTFT and the phase of DTFT.
1. Create a function template that takes a number as an argument and returns the absolute value. The absolute value of a number is the number without the sign, such that the absolute value of -5 is 5 and the absolute value of +5.0 is 5.0. Test your function with at least two numeric data types. c++
Problem IV: Find absolute value(modulus) and phase(argument) of the following complex numbers: I. z=2.
Which plot is the log-scale plot? What does the slope in the
log-scale plot mean?
1) Left plot, Log return of S&P500 index
2) Left plot, Change of S&P500 index as a dollar amount
3) Right plot, Log return of S&P500 index
4) Right plot, Change of S&P500 index as a dollar amount
5) None of them, Volatility of S&P500 index
S&P 500rGSPC) 2,271.31 .62(0.34%) Asof January 20 4:42PM EST. Market closed. S&P 600 (^GSPC) 2,271.31 7.62 (0.34%) As of...
6. Find the value of y a. log, 3) = y b. log, = y log (1125) = y d. 10° = y 15 =y 1 e 50 9. 200 7. Given the function and t f(0) = 2 g(x) = 5* Draw the 2 function. Which one grows faster with increasing & 8. Plot f(x) = log, (x) = y log2 (L) =y and g(x) =
Log-Log Plot: Take your data from Part II, and make a plot of In(T) vs. In(Meff,iot). (Ignore what the units on your axes are; that's a somewhat complicated discussion.) What should your slope be? (Hint: take the In of equation (1).) Does your actual slope agree? (This is a quantitative way of testing that we have the correct relationship, beyond just seeing that the data looks "pretty linear.") The period of an object oscillating on the end of a spring...
5. Let f(x) = e-} Log(z) (that is, f is the principal branch of z-1/2). Compute [flade, where (a) (2 points) y is the upper half of the unit circle C(0) from +1 to -1; (b) (2 points) y is the lower half of the unit circle C1(0) from +1 to -1.