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

Asked by Abhisek | 1 year ago |  131

Solution :-

Expression

(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|

$$Q[|z_1z_2|=|z_1||z_2|]$$

$$\sqrt{a^2+b^2}\times \sqrt{c^2+d^2}\times \sqrt{e^2+f^2}\times$$

$$\sqrt{g^2+h^2}=\times \sqrt{A^2+B^2}$$

By squaring

$$(a^2+b^2)(c^2+d^2)(e^2+f^2)$$

$$(g^2+h^2)(A^2+B^2)$$

Hence, proved

Answered by Pragya Singh | 1 year ago

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