Deriving properties of complex numbers

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Drag the below expressions for the argument of a complex number \(z\) to the right place so that equalities arise that are valid for any complex number.

\(2\cdot\mathrm{Re}(z)\,\mathrm{i}\)

\(2\cdot\mathrm{Re}(z)\)

\(2\cdot\mathrm{Im}(z)\,\mathrm{i}\)

\(-|z|^2\)

\(|z|^2\)

\(2\cdot\mathrm{Im}(z)\)

#z+\overline{z}=#
#\ii\cdot z-\overline{\ii\cdot z}=#
#z-\overline{z}=#
#-(\ii\cdot z+\overline{\ii\cdot z})=#
#z\cdot \overline{z}=#
#z^2-2\cdot\mathrm{Re}(z)\cdot z=#

Complex numbers: Construction of complex numbers and complex arithmetic

Deriving properties of complex numbers