Images under exp in complex plane

[erraticimpulse]

Describe the image under exp of the line with equation y = x. To do this you should find an equation (at least parametrically) for the image (you can start with the parametric form x = t; y = t), plot it reasonably carefully, and explain what happens in the limits as t approaches infinity and t approaches negative infinity.

Not very certain where I should start. Should I use rectangular coordinates or polar?

 

[erraticimpulse]

Here exp is notation for euler's number in the complex plane.

 

[shmoe]

You have the line in parametric form, are you able to write down it's image under exp(z) in parametric form?