Question

How to find z in terms of x+yi if `(z+1)/(z+2-i)` = 1 ?

Answer 1

the solution is `1-i`

Explanation:

assuming that z=x+iy we get `(x+iy+1)/(x+2+iy-1)=1` on transposing the denominator to the right side we get `x+1+iy=x+2+iy-1` on solving the left hand side nd right hand side we get 1-i

Answer 2

This equation has no solutions. See explanation.

Explanation:

The initial equation is:

`(z+1)/(z+2+i)=1`

The domain of this expression is the whole set of complex numbers except `-2-i`.

We can multiply the eqwuation by the denominator getting a linear equation.

`z+1=z+2+i`

`1=2+i`

`i=-1`

The final equality is false, so the initial equation has no solutions.