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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 34 of 52
Marks: +1, -0
For any two complex numbers z1z_1 and z2z_2, prove that
Re (z1z2)(z_1 z_2) = Re z1z_1 Re z2z_2 – Im z1z_1 Im z2z_2
Solution:  
Let z1z_1 = a + ib and z2z_2 = c + id, where a, b, c, d ∈ R
z1z2z_1z_2 = (a + ib)(c + id) = (ac – bd) + i × (bc + ad)
Re (z1z2)(z_1z_2) = ac – bd = (Re z1z_1)(Re z2z_2) – (Im z1z_1) (Im z2z_2)
Hence proved.
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