# The solution of the simultaneous equation arg(z-i)=pi/4 and arg(z-3)=pi/2 is

Solution:

$\\ arg[x+i(y-1)]=\arctan (y-1/x)=\pi /4\\ \\\Rightarrow x=y-1$

Similarly,$\\ arg[(x-3)+iy]=\arctan (y/x-3)=\pi /2\\ \\\Rightarrow x=3$

$\\ arg[(x-3)+iy]=\arctan (y/x-3)=\pi /2\\ \\\Rightarrow x=3 ;and;y=4$

$\therefore$ The desired solution is $\\ z=(3+4i)$

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