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If `sqrt(3)+i=(a+i b)//(c+i d)`, then find the value of `tan^(-1)(b//a)tan^(-1)(d//c)dot` |
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Answer» Correct Answer - `npi +(pi)/(6), n in Z` We have , `sqrt(3)+ i =(a+ ib) (c+id)` `rArr ac -bd = sqrt(3) and ad + bc = 1` Now, `tan^(-1)((b)/(a)) + tan^(-1)((d)/(c)) = tan^(-1)((b)/(a)+(d)/(c))/(1-(b)/(a)(d)/(c))` `=tan ^(-1).(bc+ad)/(ac-db)` `=tan^(-1)(1)/(sqrt(3)) = npi+(pi)/(6), n in Z` |
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