# How does a $y(t)=$plot of this exponential function looks like?

I've tried to plot the y(t) function, but there are complex numbers and I don't know how to plot it. I've been looking for hyperbolic functions transformation, but I didn't figured how to do this. My question is how to transform this in hyperbolic functions and plot it in the y vs t axes.

y(t)=(0.62*exp(-0.564*t)+1)*((-1.62+0.0749*i)/(exp((0.0510+0.24*i)*t))

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You can expand the complex exponential: $\exp((0.510+0.24i)t)=\exp(0.510t)\exp(0.24it)=\exp(0.510t)(\cos(0.24t)+i\sin(0.24t))$. Then if you multiply the numerator and denominator by $\cos(0.24t)-i\sin(0.24t)$ the denominator becomes real. You can then calculate the real and imaginary parts in a spreadsheet over whatever range you want and graph them.

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Explore it with Wolfram Alpha

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Ok thanks, but how would i do to plot in a wider range such as 0 to 50 in the time and 0 to 100 in the y ? – Kaeser May 30 '11 at 14:54

I found this to be what you might be looking for. But the results does not render anything knowledgeable when y -> {0,100}, but here is the plot anyways.

Here is the plot for only t -> {0,50}:

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