topics to study:
z=x+iy, vector representation, conjugates
triangle inequality
Re z, Im z, |z|, arg z, Arg z
polar coordinates
Euler's formula
products/quotients/conjugates in polar coordinates
roots
limits
infinite limits/limits at infinity
continuity
derivatives
Cauchy-Riemann equations
exp, sin, cos, log, Log
dt integral
contours
contour integral (dz integral)
antiderivative and related theorems
simply connected domain and related theorems
Cauchy theorem
Cauchy integral formula