For all z `in` C, prove that
(i) `(1)/(2)(z+bar(z))=Re(z),`
(ii) `(1)/(2i)(z-bar(z))=Im(z),`
(iii) `z bar(z)=|z|^(2),`
(iv) `z+bar(z))"is real",`
(v) `(z-bar(z))"is 0 or imaginary".`

if z-bar(z)=0 then z is purely imaginary

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Conjugate of a complex no and its properties. If z, z_1, z_2 are complex no.; then :- (i) bar(barz)=z (ii)z+barz=2Re(z)(iii)z-barz=2i Im(z) (iv)z=barz hArr z is purely real (v) z+barz=0implies z is purely imaginary (vi)zbarz=[Re(z)]^2+[Im(z)]^2

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If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to

If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to

If (3+i)(z+bar(z))-(2+i)(z-bar(z))+14i=0 , where i=sqrt(-1) , then z bar(z) is equal to