1.

`(a_(1)+ib_(1))(a_(2)+ib_(2))=A+iB` तो सिद्ध कीजिए कि (i) `(a_(1)^(2)+b_(2)^(2))(a_(2)^(2)+b_(2)^(2))=A^(2)+B^(2)` (ii) `"tan"^(-1)(b_(1))/(a_(1))+"tan"^(-1)(b_(2))/(a_(2))="tan"^(-1)(B)/(A)`

Answer» (i) `(a_(1)+ib_(1))(a_(2)+ib_(2))=A+iB`
`rArra_(1)a_(2)+ia_(1)b_(2)+ia_(2)b_(1)-b_(1)b_(2)=A+iB`
`rArr(a_(1)a_(2)-b_(1)b_(2))+i(1_(1)b_(2)+a_(2)b_(1))=A+iB`
`rArrA=a_(1)a_(2)-b_(1)*b_(2)` व `B=(a_(1)b_(2)+b_(1)a_(2))`
अब, `A^(2)+B^(2)` में ये मान रखने पर


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