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For any two complex numbers Z1 and Z2, prove that Re(z1z2) = Re(z2) . Re(z2) – Im(z1) . Im(z2)

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For any two complex numbers Z1 and Z2, prove that Re(z1z2) = Re(z2) . Re(z2) – Im(z1) . Im(z2)

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z1 = a + ib and z2 = c + id

z1z2 = {a + ib)(c + id) = (ac - bd) + i(ad + bc)

∴ Re(z1z2) = ac - bd

= Re(z1).Re(z2) - 1m(z1)\m{z2)

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