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I'm trying to teach myself complex analysis (I didn't have it in undergrad, and am doing my master's in France, where they all did have it in undergrad) with a book online, and one of the first exercises is causing me problems, as it isn't covered in the chapter. It's pretty trivial, so I probably should have learned it in some class a long time ago (maybe even in high school??), but I've never actually had to solve an equation like this. Here's the problem:

Find all solutions of $z^2 + 2z + (1-i) = 0$.

The answers given at the end of the book are in exponential form. I don't know many methods solving in this form, as I just learned a simple one from youtube.

Again, I'm sure it's terribly trivial, but if someone could show me how to solve this, that'd be great.

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    Excuse the question: where did you study (mathematics, I presume) that you didn't have at least one introductory course in complex analysis in undergraduate level?2012-07-11
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    Adding on Anon's comment: remember the quadratic formula applies in every field with characteristic $\,\neq 2\,$2012-07-11
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    [Wikipedia](http://en.wikipedia.org/wiki/Quadratic_equation#Generalization_of_quadratic_equation): The formula and its derivation remain correct if the coefficients $a$, $b$ and $c$ are complex numbers, or more generally members of any field whose characteristic is not 2. (In a field of characteristic 2, the element $2a$ is zero and it is impossible to divide by it.) The symbol $\pm \sqrt {b^2-4ac}$ in the formula should be understood as "either of the two elements whose square is $b^2 - 4ac$, if such elements exist".2012-07-11
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    I studied at a well-ranked public university in the midwest. They had complex analysis, but for a bachelor's degree it was a choice, and I didn't take it. I also never had topology (except a tiny bit included in Real Analysis) and taught it to myself in January before my first semester of grad school. In retrospect, I should have taken both, but I didn't realize it would be so important.2012-07-11

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