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Home / Doubts and Solutions/JEE/Mathematics

arg(z-1/z+1)=pi/4 find locus

Asked by gargpuneet989 15th August 2018, 7:31 AM
Answered by Expert
Answer:
begin mathsize 16px style arg open parentheses fraction numerator straight z minus 1 over denominator straight z plus 1 end fraction close parentheses equals straight pi over 4 arg left parenthesis straight z minus 1 right parenthesis minus arg left parenthesis straight z plus 1 right parenthesis equals straight pi over 4 straight z equals straight a plus bi arg left parenthesis straight a plus bi minus 1 right parenthesis minus arg left parenthesis straight a plus bi plus 1 right parenthesis equals straight pi over 4 tan to the power of negative 1 end exponent open parentheses fraction numerator straight y over denominator straight x minus 1 end fraction close parentheses minus tan to the power of negative 1 end exponent open parentheses fraction numerator straight y over denominator straight x plus 1 end fraction close parentheses equals straight pi over 4 tan to the power of negative 1 end exponent open parentheses fraction numerator fraction numerator straight y over denominator straight x minus 1 end fraction minus fraction numerator straight y over denominator straight x plus 1 end fraction over denominator 1 plus fraction numerator straight y over denominator straight x minus 1 end fraction cross times fraction numerator straight y over denominator straight x plus 1 end fraction end fraction close parentheses equals straight pi over 4 fraction numerator 2 straight y over denominator left parenthesis straight x minus 1 right parenthesis left parenthesis straight x plus 1 right parenthesis plus straight y squared end fraction equals 1 straight x squared plus straight y squared minus 2 straight y minus 1 equals 0 This space is space circle space with space centre space left parenthesis 0 comma space 1 right parenthesis space and space straight r equals square root of 2 end style
Answered by Expert 16th August 2018, 10:34 AM
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