Oh now I see... Neat. 
But you then need to have different ranges for the x variable.


using Plots

x = linspace(-2, 2, 100)
xh = linspace(0, 2, 50)
xk = linspace(-2, 0, 50)

f =  sqrt(complex(4 .- x.^2))
g = -sqrt(complex(4 .- x.^2))
h = sqrt(complex(-xh.^2 .+ 2 * xh))
k = -sqrt(complex(-xk.^2 .- 2 * xk))

plot(real(f), x)
plot!(real(g), x)
plot!(real(h), xh)
plot!(real(k), xk, show=true)
readline()

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