Argh ok a couple of clues here would be useful !
Let f(z) = 5i(z + i)
1 - Describe the effect f has on a typical point of C in terms of geometric transformations.
Is it that it is scaled by a factor of 5, moved up 1 unit and rotated by 90 degrees ?
2 - Let GAMMA be the path with the parametrization
gamma(t) = 2 - i + 3e^it
Sketch GAMMA indicating the direction of increasing t and identifying
its initial and final points in cartesian form.
So I change 3e^it to 3(cost + isint) ?
So I get 2-i+3(cost + isint)
Then do i need to get the real and imaginary parts for the parametric equations I think ?
3 - By applying your geometric description of the function f to GAMMA, sketch the path f(GAMMA). Indicate the direction of f(GAMMA) and identify it's inital and final points in Cartesian form.
4 - Write down the standard parametrization of f(GAMMA)
Bit stuck on 3 and 4.
5 - Let f(z) = exp(1-2iz)
g(z) = Log(1-2iz)
h(z) = (1-2iz)^3i
a - write down the domain of each of the functions f,g and h
f would be all complex numbers.
In g the part 1-2iz would have to be positive but I'm not sure how I describe that.
Similar case for h
b - Explain why f does not have an inverse fucntion.
Because of the periodicity e^z+2piei = e^z
c - Show that g has an inverse function and find it's domain and rule
Any clues pointers appreciated cheers !