MHB Plotting complex equations on the Argand plane with Wolfram Alpha

[Saitama]

I am wondering how one would go about drawing graphs in Argand plane using Wolfram Alpha. For instance, I want to plot an ellipse $|z-1|+|z+1|=5$ using W|A, what should be the input? Simply entering $|z-1|+|z+1|=5$ doesn't give what I want.

Thanks!

 

[Deveno]

Wolfram|Alpha doesn't seem to do well with complex plots.

What I would do is take the square root of the modulus and turn it into a "real" plot, like so:

$\sqrt{(x-1)^2 + y^2} + \sqrt{(x+1)^2 +y^2} = 5$

 

[Saitama]

Wolfram|Alpha doesn't seem to do well with complex plots.

What I would do is take the square root of the modulus and turn it into a "real" plot, like so:

$\sqrt{(x-1)^2 + y^2} + \sqrt{(x+1)^2 +y^2} = 5$

Yes, I know I can enter that but that was just an example I stated in my post. How would I go about plotting

$$(z-1)^{25}=2\omega^2(z+1)^{25}$$