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: (a 2 + b 2 ) (c 2 + d 2 ) (e 2 + f 2 ) (g 2 + h 2 ) = A 2 + B 2

Philoid · Accepted Answer

It is given in the question that,

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

Using, [|z₁z₂|=|z₁||z₂|]

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

Now, we will square on both sides,

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

Hence, proved

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