Question Number 51216 by gunawan last updated on 25/Dec/18
$$\mathrm{show}\:\mathrm{lim}\:{f}\left({z}\right)\:\mathrm{for}\:{z}\rightarrow\mathrm{0}\:\mathrm{along}\:\mathrm{the}\:\mathrm{line}\:{y}={x} \\ $$$$\mathrm{where}:\:{f}\left({z}\right)=\frac{\mathrm{2}{xy}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }−{i}\frac{{y}^{\mathrm{2}} }{{x}^{\mathrm{2}} } \\ $$
Answered by kaivan.ahmadi last updated on 11/Jan/19
$$\mathrm{lim}\frac{\mathrm{2x}^{\mathrm{2}} }{\mathrm{2x}^{\mathrm{2}} }−\mathrm{i}\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }=\mathrm{1}−\mathrm{i} \\ $$