That's a fun problem. I say start by defining z=a+ib where a and b are real numbers and also note z=|z|exp(i[itex]\Phi[/itex]) the polar form of z, so that you're looking for the solutions to
[tex]|z|e^{i\Phi}=e^{-a-ib}[/tex]
And use the fact that two complex numbers are equal iff their modulus are the same and their polar angle are the same up to a difference of [itex]2n\pi[/itex], [itex]n\in\mathbb{Z}[/itex].
We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling We Value Civility
• Positive and compassionate attitudes
• Patience while debating We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving