Q.1 If modulus of 1-iz/z-i=1 , find the locus of z

 

 

Take z = x+iy

modulus of(1-iz)/(z-i) = 1

By theorem ,

modulus of 1-i(x+iy) = modulus of x+iy - 1

sqrt((y+1)²+x²) = sqrt((x-1)²+y²)

Squaring both sides

y²+1+2y+x²=x²+1-2x+y²

x+y=0

the locus of the given expression is a straight line passing thru the origin

 

Hey,krish.

Ur ans needs a bit of editing.

The denom is z-i not z-1.

So, on simplification, u get locus of z as y=0.

i.e;z is a real no. &lies on real axis (x-axis) .

let z=x+iy therefore 1-(x+iy)/x+i(y-1) as we know that whole mod of numerator & denominator is equal to the individual mod of numerator mod of denominator & numerator in case of complex number therefore taking individual mod

(1+y)²+x²/x² +(y-1)² = 1 on solving we get y=o thus the locus is x-axis