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## Main Question or Discussion Point

Hello,

I would like your help understanding how to map a region of the space [itex] \mathbb{C}^2 [/itex] spanned by two complex conjugate variables to the real plane [itex] \mathbb{R}^2 [/itex] .

Specifically, let us think that we have two complex conugate variables [itex] z [/itex] and [itex] \bar{ z} [/itex] and we define a triangle in the space represented schematically by having [itex] z [/itex] in the abscissa and [itex] \bar{z} [/itex] in the ordinate. I know this [itex] \mathbb{C}^2 [/itex] space shold be isomorphic to [itex] \mathbb{R}^4[/itex] , but considering the constraint that the variables are conjugate, I am hopping one can map such region to a representation in [itex] \mathbb{R}^2 [/itex] .

Many thanks!

I would like your help understanding how to map a region of the space [itex] \mathbb{C}^2 [/itex] spanned by two complex conjugate variables to the real plane [itex] \mathbb{R}^2 [/itex] .

Specifically, let us think that we have two complex conugate variables [itex] z [/itex] and [itex] \bar{ z} [/itex] and we define a triangle in the space represented schematically by having [itex] z [/itex] in the abscissa and [itex] \bar{z} [/itex] in the ordinate. I know this [itex] \mathbb{C}^2 [/itex] space shold be isomorphic to [itex] \mathbb{R}^4[/itex] , but considering the constraint that the variables are conjugate, I am hopping one can map such region to a representation in [itex] \mathbb{R}^2 [/itex] .

Many thanks!