The equation |z-i| = |z-1|, i = √-1, represents?

Correct option is D. The line through the origin with slope 1
Let z = x + iy
|z - i| = |z - 1|
|x + i(y - 1)| = |(x - 1) + iy|
√(x² + (y - 1)²) = √((x - 1)² + y²)
x² + (y - 1)² = (x - 1)² + y²
x² + y² - 2y + 1 = x² - 2x + 1 + y²
-2y = -2x
y = x
The line through the origin with slope 1
Hence option (d) is correct.