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Equation in complex numbers

I need to solve the following equation.

solve(z^2 == (1-sqrt(3)*I)*z.conjugate(), z)

Sage says

[z == -sqrt((-I*sqrt(3) + 1)*conjugate(z)), z == sqrt((-I*sqrt(3) + 1)*conjugate(z))]

I'd like to get solutions in polar form, something like

[z == 0, z == 2*e^(pi*I/9), z == 2*e^(7*pi*I/9), z == 2*e^(13*pi*I/9)]

Or I'd like to get the absolute values and arguments of the solutions. Is it possible in Sage?