All the derivation of the equation of line on complex plane uses the fact that (x,y) \in R^2 can be identified with x+iy \in C.(adsbygoogle = window.adsbygoogle || []).push({});

Thus, they begin with ax+by+c = 0 then re-write x = (z+\bar{z})/2 and y = (z-\bar{z})/(2i), and substitute it into real plane line equation to get it in complex form.

What I don't quite understand is, since (x,y) is identified with (x,iy),

don't we need to write ax+by+c=0 into ax+biy+c=0 before we proceed with the substitution? Why don't we need to do such thing?

Thank you.

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# Equation of a line in complex plane

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