If \( (a+i b)(c+i d)(e+i f)(g+i h)=A+i B \), then show that \[ \lef...

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