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

Question : 34

Total: 52

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

Solution:

Let z1 = a + ib and z2 = c + id, where a, b, c, d ∈ R
z1z2 = (a + ib)(c + id) = (ac – bd) + i × (bc + ad)
Re (z1z2) = ac – bd = (Re z1)(Re z2) – (Im z1) (Im z2)
Hence proved.

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