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

Question

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

Shiksha Nation · Accepted 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|

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

On squaring both sides, we obtain:

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

Hence, proved.

Verified Answer