Properties of complex numbers

let  z=\[a+ib\]  then its conjugate is given by z'= \[ a-ib\]

zz' = \[|z|^2\]  where \[|z|\] is modulus of complex number z

zz'=\[a^2+b^2\]

Example z=2-i3 then zz'=\[2^2+3^2=13\]

              z=\[ \frac{1}{\sqrt{2}}+i\frac{\sqrt{3}}{2}\]  then zz'=\[ (\frac{1}{\sqrt{2}})^2+i(\frac{\sqrt{3}}{2})^2=\frac{5}{4}\]

               

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