Question

Z=x+iy and |1-iz|÷|z-i|=1, then z lies on

Answer 1

Given:

Z=x+iy and |1-iz|÷|z-i|=1, then z lies on

To find:

z lies on

Solution:

From given, we have,

Z=x+iy and |1-iz|÷|z-i|=1

now consider,

|1 - iz| ÷ |z - i| = 1

substitute the value of z in the above equation, we get,

|1 - i(x + iy)| ÷ |(x + yi) - i| = 1

|1 - ix + y| ÷ |x + yi - i| = 1

(1 + y) - i (x) = x + i (y - 1)

(1 + y) = x

x -  y = 1  ...(1)

and

- x = y - 1

x + y = 1 ...(2)

adding equations (1) and (2), we get,

2x = 2

x = 1

substituting the value of x in one of the above equations, we get,

1 - y = 1

1 - 1 = y

y = 0

z lies on the point of intersection of the lines, x = 1 and y = 0.

z lies on a point (1, 0)