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If \( (x+i y)(p+i q)=\left(x^{2}+y^{2}\right) i \), then, where \( x, y, p, q \in R: \)
(1) \( p=x, q=y \)
(2) \( p=x^{2}, q=y^{2} \)
(3) \( x=q, y=p \)
(4) \( x=-q, y=p \)
\( \mathrm{P} \)
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