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For any two complex numbers `z_1`and `z_2`, prove that `Re(z_1z_2)=Re(z_1) Re(z_2)-Im(z_1) Im(z_2)`.

Text Solution

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Let `z1​=a+ib`
and `z2​=x+iy`
So,`z1​z2​=(a+ib)(x+iy)`
`=>z1​z2​=(ax−by+i(bx+ay))`
`=>Re(z1​z2​)=ax−by`
thus,`Re(z1​z2​)=Rez1​Rez2​−Imz1​Imz2​`
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