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Question

On which axis does the complex numberz=x+iywhich satisfy the equation mod(z-5iz+5i)lie?


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Solution

Given equationz-5iz+5i=1

Complex numberz=x+iy

On substitutingz=x+iyin given equation, we get

x+iy-5ix+iy+5i=1x+i(y-5)x+i(y+5)=1x2+y-52x2+(y+5)2=1x2+(y-5)2=x2+(y+5)2

On squaring on both sides we get

x2+(y-5)2=x2+(y+5)2(y-5)2=(y+5)2-10y=10y-20y=0y=0

Hence the point lies onX-axis.


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