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प्रश्न
For any two complex numbers z1 and z2, prove that Re (z1z2) = Re z1 Re z2 – Imz1 Imz2
उत्तर
Let z1 = a + ib, z2 = c + id
∴ z1z2 = (a + ib)(c + id)
= ac + adi + bci + i2bd
= (ac – ba) + (ad + bc) i [∴ i2 = – 1]
Real part of Re(z1z2) = ac – bd
= Rez1 Rez2 – Imz1 Imz2
Here real part of Rez1 = a, similarly Rez2 = c
Imz1 = imaginary part of z1 = b
Similarly Imz2 = d.
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