locus (1 Viewer)

[hasterz]

W = z/(z+1)
if z is purely imaginary find the locus of W

 

[shafqat]

I'm a bit rusty, but here goes.
x + iy / x + iy + 1 *( x + 1 - iy/ x + 1 – iy)
= x^2 + x + iy + y^2/ (x+2)^2 + y^2
So as real part is 0, x^2 + x + 1/4 + y^2 = 1/4
So (x+1/2)^2 + y^2 = 1/4
Alternativey as it is imaginary, arg is pi/2 or -pi/2. So the locus is a circle with diameter from - 1 to 0, which gives the locus above.

 

[hasterz]

thanks dude but the question is asking to find the locus of W not z

 

[shafqat]

Sorry I read it completely backwards. Rearrange the equation to make z the subject, and then repeat the method I used.

 

[justchillin]

For these questions dude just let z=x+iy then rearrange everything... then just take the condition... ie for this question Re(z)=0... it'll come out beautifully...