e^(1-i)*e^(2+2i) = e^(1-i + 2 + 2i) = e^(3 + i)
Now to get this into the for a+bi, we need to know that:
e^(i theta) = cos(theta) + i sin(theta)
for real theta.
e^(3+i)=e^3 e^(i) = e^3 [cos(1) + i sin(1)] = e^3 cos(1) + i e^3 sin(1).
(Note trig function are in radians)
e is a real number a bit like pi, and e ~= 2.718282. Like pi it is important2
Im feeling lost when dealing with e. I don't know what im doing, I don't know what it is and where it comes from. All i know is that is got something to do with exponetial growth.
in mathematics because it has special properties, one of which is that:
d/dx (e^x) = e^x.