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Need help plotting $0\leq t\leq 2\pi$, $z(t)=e^{(1+i)t}$ and $z(t)=e^{(-1+i)t}.$ How can I plot them online or any software that I should use to get the graph of such curves? I am familiar with Wolfram but not able to get this.

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    @Moo I suspect that he wants the parametric curve lying in the complex plane, rather than the graphs of the real valued functions of the real and imaginary parts of $z(t)$. – 2017-01-15

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Specify that you want a parametric plot and explicitly break it up into the real and imaginary parts like so:

parametric plot (Re(exp((-1+i)*t)), Im(exp((-1+i)*t)), t=0..2pi)

That input yields the following:

enter image description here