Express the following expression in the form of \( a+i b \) : \[ \f...

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Express the following expression in the form of \( a+i b \) :
\[
\frac{(3+i \sqrt{5})(3-i \sqrt{5})}{(\sqrt{3}+\sqrt{2} i)-(\sqrt{3}-i \sqrt{2})}
\]
(IV)
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