If \( (a+i b)(c+i d)(e+i f)(g+i h)=\mathrm{A}+i \mathrm{~B} \), the...

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If \( (a+i b)(c+i d)(e+i f)(g+i h)=\mathrm{A}+i \mathrm{~B} \), then
show that
\[
\left(a^{2}+b^{2}\right)\left(c^{2}+d^{2}\right)\left(e^{2}+f^{2}\right)\left(g^{2}+h^{2}\right)=\mathrm{A}^{2}+\mathrm{B}^{2} .
\]
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