- #1

timon

- 56

- 0

## Homework Statement

Sketch the set of complex numbers

*z*for which the following is true:

arg[(z+i)/(z-1)] = [tex]\pi[/tex]/2

## Homework Equations

if z=a+bi then

arg(z) = arctan(b/a)

**[1]**

and if Z and W are complex numbers then

arg(Z/W) = arg(Z) - arg(W)

**[2]**

## The Attempt at a Solution

using eq. [2] i wrote:

arg(z+i) - arg(z-1) = [tex]\pi[/tex]/2

thus, using eq. [1]

arctan[(b+1)/a] - arctan[(b/(a-1)] = [tex]\pi[/tex]/2

But then I got stuck on how to solve for Z. I tried to guess using a table of exact trig values: arctan([tex]\sqrt{3}[/tex]/3) - arctan(1) = [tex]\pi[/tex]/2 seemed like a possible solution, but solving for a and b gives b=-1 and a=0, which is not a solution. Any help is much appreciated.