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  • 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

Q : 19      If   \small (a+ib)(c+id)(e+if)(g+ih)=A+iB,  then show that                                     \small (a^2+b^2)(c^2+d^2)(e^2+f^2)(g^2+h^2)=A^2+B^2

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best_answer

It is given that
\small (a+ib)(c+id)(e+if)(g+ih)=A+iB,
Now, take  mod on both sides 
\left | (a+ib)(c+id)(e+if)(g+ih) \right |= \left | A+iB \right |
|(a+ib)||(c+id)||(e+if)||(g+ih)|= \left | A+iB \right |                                   (\because |z_1z_2|=|z_1||z_2|)
(\sqrt{a^2+b^2})(\sqrt{c^2+d^2})(\sqrt{e^2+f^2})(\sqrt{g^2+h^2})= (\sqrt{A^2+B^2})
Square both the sides. we will get

({a^2+b^2})({c^2+d^2})({e^2+f^2})({g^2+h^2})= (A^2+B^2)

Hence proved

Posted by

Gautam harsolia

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