Find the image of the rectangle with four vertices A=0, B= pi*i, C= -1+pi*i, D = -1 under the function f(z)=e^x
2. The attempt at a solution
So, the graph of the original points is obvious.
Now I have to map them to the new function.
Seems easy enough, but I am not getting one step. Can someone help me get started?
We have f(z) = e^x
So is it as simple as letting A = 0 = z = e^0 aka 1.
B = pi*i so z = pi+i so f(z) = e^(pi*i) aka cos(pi)+i*sin(pi) = -1
C = -1*pi*i so z = -1+pi*i and thus e^(-1+pi*i) = (1/e)*e^(pi*i) = -1/e
D = -1 so z = -1 and e^(-1) = 1/e
Thus we'd have points (0, 1) = A, (pi*i, -1) = B, (-1+pi*i, -1/e) = C, (-1, 1/e) = D
Not sure how i'd graph C tho :/