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For any two complex numbers z1and z2, pr...

For any two complex numbers `z_1`and `z_2`, prove that `R e(z_1z_2)=R ez_1R e z_2-|m z_1|m z_2`.

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The correct Answer is:
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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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NAGEEN PRAKASHAN ENGLISH-COMPLEX NUMBERS AND QUADRATIC EQUATION -MISCELLANEOUS EXERCISE
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  10. If z1=2-i ,z2=1+i ,find |(z1+z2+1)/(z1-z2+i)|

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