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Question Number 551 by 123456 last updated on 26/Jan/15

f(z)=z(y−xi)  z=x+yi  (df/dz)=?

$${f}\left({z}\right)={z}\left({y}−{xi}\right) \\ $$$${z}={x}+{yi} \\ $$$$\frac{{df}}{{dz}}=? \\ $$

Answered by prakash jain last updated on 26/Jan/15

y−xi=−i(x+iy)=−iz  z(y−ix)=−iz^2   (df/dz)=−2iz=−2i(x+iy)=2y−i2x

$${y}−{xi}=−{i}\left({x}+{iy}\right)=−{iz} \\ $$$${z}\left({y}−{ix}\right)=−{iz}^{\mathrm{2}} \\ $$$$\frac{{df}}{{dz}}=−\mathrm{2}{iz}=−\mathrm{2}{i}\left({x}+{iy}\right)=\mathrm{2}{y}−{i}\mathrm{2}{x} \\ $$

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