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Math Help - Complex exponential signal?

  1. #1
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    Complex exponential signal?

    Complex exponential signal?

    Ive been out of school for about 15 years. I am taking a discrete course online and have this homework problem. I don't know where to start. I am working with my old diff eq books to get caught up but need help.

    Given the complex exponential signal: y(t)=3*exp(j*pi/3)*exp(j*10*pi)
    a) What is the imaginary part i(t)?
    b)What are the frequency and period of i(t)?
    c)What is the real part r(t)?
    d)What is the value of r(t) at t=10ms?
    e) At what time incidents does r(t) reach maximum or minimum?
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  2. #2
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    Re: Complex exponential signal?

    Hey PrimalScream.

    Hint: You will need to put the function in various forms. z = x + iy gives you real and complex parts x and y respectively and r*e^(ix) = rcos(x) + i*rsin(x). Also remember that e^a * e^b = e^(a+b).
    Thanks from PrimalScream and topsquark
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  3. #3
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    Re: Complex exponential signal?

    I made a mistake typing the original problem. It's y(t)=3*exp(j*pi/3)*exp(j*10*pi*t). Would this mean that:
    y(t)=3*exp((j*pi/3)+(j*10*pi*t)) then 3*cos((pi/3)+(10*pi*t)) + jsin((pi/3)+(10*pi*t))

    Thanks
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  4. #4
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    Re: Complex exponential signal?

    If you have y = 3*exp(j[pi/3 + 10pi*t]) then this is equal to 3*[cos(pi/3+10*pi*t) + i*sin(pi/3+10*pi*t)] (i = j if you are an electrical engineer).

    So are you spot on.
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  5. #5
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    Re: Complex exponential signal?

    thanks
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