The complex number $z$ which satisfies the condition $\left|\dfrac{z+i}{z-1}\right| = 1$ lies on
🎥 Video solution / Text Solution of this question is given below:
Let $z = x + iy$
Then $\left|\dfrac{z+i}{z-1}\right| = 1 \Rightarrow |z+i| = |z-1|$
$\Rightarrow (x)^2 + (y+1)^2 = (x-1)^2 + y^2$
$\Rightarrow 2x = 1 - 2y$
$\Rightarrow x + y = \dfrac{1}{2}$
Hence the locus is a straight line.