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We are given three complex numbers a,b,and c. Consider $Re(az^{2} + bz +c)=0$. What is this curve? I am having a hard time approaching this problem. Any suggestions or help would be great.

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    See [this](http://math.stackexchange.com/questions/60801).2011-09-11

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If $a=a_1+ia_2$, $b=b_1+ib_2$, $c=c_1+ic_2$ and $z=x+iy$, then $z^2=x^2-y^2+2ixy$ hence $az^2+bz+c$ equals $ a_1(x^2-y^2)-2a_2xy+b_1x-b_2y+c_1+i\cdot(\text{something real}), $ and you are done.