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Sir pls solve the following.
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Asked by rsudipto | 28 Dec, 2018, 19:53: PM
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begin mathsize 12px style z subscript 1 space equals space 2 space e to the power of i theta end exponent space z subscript 2 space equals space 3 space e to the power of i left parenthesis theta plus pi over 3 right parenthesis end exponent z subscript 1 plus z subscript 2 space equals space 2 space e to the power of i theta end exponent space plus space 3 space e to the power of i left parenthesis theta plus pi over 3 right parenthesis end exponent space space equals space e to the power of i theta end exponent open curly brackets 2 space plus space 3 e to the power of i pi over 3 end exponent close curly brackets space equals space e to the power of i theta end exponent open curly brackets 2 plus 3 open parentheses 1 half plus i fraction numerator square root of 3 over denominator 2 end fraction close parentheses close curly brackets space equals space e to the power of i theta end exponent over 2 open curly brackets space 7 plus i space 3 square root of 3 space close curly brackets space....... left parenthesis 1 right parenthesis z subscript 1 minus z subscript 2 space equals space 2 space e to the power of i theta end exponent space minus space 3 space e to the power of i left parenthesis theta plus pi over 3 right parenthesis end exponent space space equals space e to the power of i theta end exponent open curly brackets 2 space minus space 3 e to the power of i pi over 3 end exponent close curly brackets space equals space e to the power of i theta end exponent open curly brackets 2 minus 3 open parentheses 1 half plus i fraction numerator square root of 3 over denominator 2 end fraction close parentheses close curly brackets space equals space e to the power of i theta end exponent over 2 open curly brackets space 1 minus i space 3 square root of 3 close curly brackets space........ left parenthesis 2 right parenthesis fraction numerator z subscript 1 plus z subscript 2 over denominator z subscript 1 minus z subscript 2 end fraction space equals space fraction numerator space 7 plus i space 3 square root of 3 over denominator space 1 minus i space 3 square root of 3 end fraction space........... left parenthesis 3 right parenthesis L e t space u s space m u l t i p l y space b o t h space n u m e r a t o r space a n d space d e n o m i n a t o r space o f space e q n. left parenthesis 3 right parenthesis comma space b y space c o n j u g a t e space o f space d e n o m i n a t o r T h e n space fraction numerator z subscript 1 plus z subscript 2 over denominator z subscript 1 minus z subscript 2 end fraction space equals 1 over 7 open parentheses negative 5 plus i space 6 square root of 3 close parentheses h e n c e space open vertical bar fraction numerator z subscript 1 plus z subscript 2 over denominator z subscript 1 minus z subscript 2 end fraction close vertical bar space equals space 1 over 7 square root of 25 plus 108 end root space equals space square root of 19 over 7 end root end style
Answered by Thiyagarajan K | 30 Dec, 2018, 17:52: PM

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