NCERT Solution Class XI Mathematics Complex Numbers and Quadratic Equations Question 19 (Mis Ex)

Question 19:

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2.

Answer

(a + ib) (c + id) (e + if) (g + ih) =A + IB’

∴ |(a + ib) (c + id) (e + if) (g + ih)| = |A + iB|

⇒ |(a + ib) ×|(c + id)| × |(e + if | × |(g + ih)| = |A + iB|   [|z1z2| = |z1||z2|]

On squaring both sides, we obtain

(a2 + b2) (c2 + d2) (e2 + f2) (g2 + h2) = A2 + B2

Hence, proved.

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