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