# Complex numbers

posted by .

For the transformation w=(z+i)/(z-i)
show that as z moves along the real axis, w moves along a circle centre O and radius 1

I do not know where to start

changing it to polar form will help

w=magnitude @ (arctan 1/z - arctan -1/z)

where magnitude is sqrt (z^2+1)/(z^2+1)

or
w= 1 @ (2 arctan 1/z)

Is that a circle?
check my thinking.

I am really sorry but I do not understand your notation

## Similar Questions

1. ### Maths again

For the transformation w=z^2, show that as z moves once round the circle centre O and radius 2, w moves twice round centre O radius 4. I am okay finding the radius and centre of the locus but how do I show it moves twice roundfor w …
2. ### physics # 1

1. If a particle moves in a plane so that its position is described by the function x = Acosùt, and y = Asinùt, it is a.) moving with varying speed along a circle b.) moving with constant speed along a circle c.) moving with constant …
3. ### Calculus--complex numbers

let z= a+bi be a complex number. it is given that the quotient (z-i)/(z-1) is purely imaginary. show that z lies on a circle and determine the centre and radius of this circle. OK, here's my working out...( i am using "X" as my times …
4. ### physics

an object moves along a circle of radius r. its start froam A and reaches B. what is the path length?
5. ### Physics

A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 200g piece moves along the x-axis with a speed of 2.00m/s and a 235g piece moves along the the y axis …
6. ### Physics

A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 200g piece moves along the x-axis with a speed of 2.00m/s and a 235g piece moves along the the y axis …
7. ### Calculus

1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A …
8. ### Calculus

1. The radius of a sphere is expanding at a rate of 14 in/min. a) Determine the rate at which the volume is changing when the radius is 8 in. b) Determine the rate at which the surface area is changing when the radius is 8 in. 2. A …
9. ### Polar, Cylindrical, and Spherical Coordinates

Let C be a circle that passes through the origin. Show that we can find real numbers s and t such that C is the graph of r = 2s*cos(theta + t) I think that I could start by writing it like R^2=(x-h)^2+(y-k)^2 where R is the radius …
10. ### physics

An unstable nucleus with a mass of 18.0 ✕ 10-27 kg initially at rest disintegrates into three particles. One of the particles, of mass 5.0 ✕ 10-27 kg, moves along the positive y-axis with a speed of 9.0 ✕ 106 m/s. Another particle, …

More Similar Questions