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## Main Question or Discussion Point

So I know that a complex number can be represented by ##z=x+iy##, where ## z = x + iy \in \mathbb{C}##.

Would it be okay to then state that ## z = x + iy \in \mathbb{C} := (x,y) \in \mathbb{R}^2 ##?

If we can just look at complex numbers as coordinates in ##\mathbb{R}^2## what is the point of even defining a complex plane? (just started learning these math logic notations, so pardon me if my intuition is incorrect)

Would it be okay to then state that ## z = x + iy \in \mathbb{C} := (x,y) \in \mathbb{R}^2 ##?

If we can just look at complex numbers as coordinates in ##\mathbb{R}^2## what is the point of even defining a complex plane? (just started learning these math logic notations, so pardon me if my intuition is incorrect)