I am trying to plot a function (real and imaginary part) without the use of graphing software.
My question is: if $f(t) = 0$ for $t<0$ and $f(t) = Ae^{-λt}$ for $t\ge0$ $(λ>0)$ ,
I found the Fourier Transform of $f(t)$: $g(w) = \frac{A}{\sqrt{2\pi}} (\frac{λ}{λ^2+w^2} - \frac{iw}{λ^2+w^2})$
Now I am trying to plot the real part $ \frac{A}{\sqrt{2\pi}} (\frac{λ}{λ^2+w^2})$ and also the imaginary part: $g(w) = \frac{A}{\sqrt{2\pi}} (- \frac{iw}{λ^2+w^2})$
What are the processes I need to think about to think of how will the shape will look like to figure out the graph?