Exercise $1-2$: Please compute an analytic expression, by hand, for the real and imaginary parts of the following complex functions. Please also plot these in python or Matlab for $t=0$:$\mathrm{.}01$:$10.$ Include both your plotting code and your analytical work in the pdf you submit to show your work.

$($a$)f(t)=e^{-it}.$

$($b$)f(t)=e^{(1+i)t},$

$($c$)f(t)=2e^{(-1-i)t}$

$($d$)f(t)=e^{(-1+2i)t}.$