I am having a few issues with Complex Analysis. I've done as much as I could on a few practice problems hoping I would understand it but I'm a bit stuck.

1) Find a parameterization of the line segment joining

and

. Find the image of the segment under the mapping

.

This is what I did:

and

for

The graph doesn't look look right. I've reworked it a few times and I keep getting the same answer. Am I making a silly algebraic mistake somewhere?

2)Find the image

of the set

under the given complex mapping

;

is the line

A friend told me to do it this way: *Is this correct?*

I'll just submit the two problems I'm having the most problem with. Thanks for looking at this.