InterviewSolution
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InterviewSolution
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If `(a+i b)/(c+i d)=x+i y ,`prove that `(a-i b)/(c-i d)=x-i ya n d(a^2+b^2)/(c^2+d^2)=x^2+y^2dot` |
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Answer» `(i) ((a+ib)/(c+id))=(x+iy) rArr (bar((a+ib)/(c+id)))=bar((x+iy))` `" " rArr bar((a+ib))/(bar(c+id))=(x+iy)rArr ((a-ib))/((c-id))=(x-iy)`. (ii) We have `((a+ib))/((c+id))=(x+iy) and ((a-ib))/((c-id))=(x-iy)` `rArr" "((a+ib))/((c+id))xx((a-ib))/((c-id))=(x+iy)(x-iy)` `rArr" "((a+ib)(a-ib))/((c+id)(c-id))=(x+iy)(x-iy)` `rArr" "((a^(2)+b^(2)))/((c^(2)+d^(2)))=(x^(2)+y^(2))`. |
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