Show the following concerning the exponential map.
((a)) The image of the line {(x,y):x=t,y=2π+t}, where −∞<t<∞ is a spiral.
((b)) The image of the first quadrant {(x,y):x>0,y>0} is the region {w:∣w∣>1}.
((c)) If a is a real constant, the horizontal strip {(x,y):α<y≤α+2π} is mapped one-to-one and onto the nonzero complex numbers.
((d)) The image of the vertical line segment {(x,y):x=2,y=t}, where 6π<t<67π is half a circle.
((e)) The image of the horizontal ray {(x,y):x>0,y=3π} is a ray.