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?

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).

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

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.

Re: Complex exponential signal?