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Prove that Re (z1 z2)= Re z1 Re z2 - Imz...

Prove that `Re (z_1 z_2)= Re z_1 Re z_2 - Imz_1 Imz_2` ,

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Let `z_(1)=x_(1)+iy_(1) and z_(2)=x_(2)+iy_(2)`
`z_(1)z_(2)=(x_(1)+iy_(1))(x_(2)+iy_(2))`
`" " =x_(1)x_(2)+i(x_(1)y_(2) +x_(2)y_(1 ))+i^(2) y_(1)y_(2 )`
`" "=(x_(1) x_(2)-y_(1)y_(2))+i( x_(1)y_(2)+x_(2)y_(1))`
Then, real part of `z_(1)z_(2)`
`Re(z_(1)z_(2))=(x_(1)x_(2)-y_(1)y_(2))`
`" "=Rez_(1)Rez_(2)- Im z_(1)Imz_(2)`
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