Complex Mapping - Express x & y in terms of u & v

[evermore]

w = 1/(z+2j): w = u + jv, z = x+jy

Its not hard to express this in terms of z... z = 1/w - 2j
But how can i go about expressing x and y and terms of u and v
Substitution of those above terms gets you

x + jy = 1/(u + jv) - 2j

I am not clear on the next steps
Any help is much appreciated.
Thankyou

 

[HallsofIvy]

w = 1/(z+2j): w = u + jv, z = x+jy

Its not hard to express this in terms of z... z = 1/w - 2j
But how can i go about expressing x and y and terms of u and v
Substitution of those above terms gets you

x + jy = 1/(u + jv) - 2j

I am not clear on the next steps
Any help is much appreciated.
Thankyou

Get that fraction into a+ jb form by multiplying numerator and denominator by the complex conjugate of u+ jv:
x+ jy= (u- jv)/(u²+ v²)- 2j

Now separate into real and imaginary parts:
x= u/(u^2+ v^2), y= -v/(u^2+ v^2)- 2.

(I can't tell you how much it hurt to write "j" instead of "i". Blast these engineers and their jmaginary numbers!)

 

[Swapnil]

We are the infamous Electrjcal Engjneers..