Question Number 551 by 123456 last updated on 26/Jan/15
$${f}\left({z}\right)={z}\left({y}−{xi}\right) \\ $$$${z}={x}+{yi} \\ $$$$\frac{{df}}{{dz}}=? \\ $$
Answered by prakash jain last updated on 26/Jan/15
$${y}−{xi}=−{i}\left({x}+{iy}\right)=−{iz} \\ $$$${z}\left({y}−{ix}\right)=−{iz}^{\mathrm{2}} \\ $$$$\frac{{df}}{{dz}}=−\mathrm{2}{iz}=−\mathrm{2}{i}\left({x}+{iy}\right)=\mathrm{2}{y}−{i}\mathrm{2}{x} \\ $$