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ques no 26

Asked by chandanbr6004 9th November 2017, 7:15 AM
Answered by Expert
Answer:
open parentheses fraction numerator straight z plus 2 over denominator straight z minus 4 straight i end fraction close parentheses equals open parentheses fraction numerator straight x plus iy plus 2 over denominator straight x plus iy minus 4 straight i end fraction close parentheses equals equals open parentheses fraction numerator left parenthesis straight x plus 2 right parenthesis plus iy over denominator straight x plus straight i left parenthesis straight y minus 4 right parenthesis end fraction close parentheses
rationalizing
equals open parentheses fraction numerator left parenthesis straight x plus 2 right parenthesis plus iy over denominator straight x squared plus left parenthesis straight y minus 4 right parenthesis squared end fraction close parentheses open parentheses straight x minus straight i left parenthesis straight y minus 4 right parenthesis close parentheses
equals fraction numerator left parenthesis straight x plus 2 right parenthesis straight x plus straight y left parenthesis straight y minus 4 right parenthesis minus straight i left parenthesis xy minus left parenthesis straight y minus 4 right parenthesis left parenthesis straight x plus 2 right parenthesis right parenthesis over denominator straight x squared plus left parenthesis straight y minus 4 right parenthesis squared end fraction
seperating space real space and space imaginary space part
equals fraction numerator left parenthesis straight x plus 2 right parenthesis straight x plus straight y left parenthesis straight y minus 4 right parenthesis over denominator straight x squared plus left parenthesis straight y minus 4 right parenthesis squared end fraction minus fraction numerator straight i left parenthesis xy minus left parenthesis straight y minus 4 right parenthesis left parenthesis straight x plus 2 right parenthesis right parenthesis over denominator straight x squared plus left parenthesis straight y minus 4 right parenthesis squared end fraction
now
tanθ equals straight pi over 2 space
rightwards double arrow straight theta equals infinity
so space the space denominator space should space be space equal space to space zero space ie. space real space part space is space equal space to space zero
fraction numerator left parenthesis straight x plus 2 right parenthesis straight x plus straight y left parenthesis straight y minus 4 right parenthesis over denominator straight x squared plus left parenthesis straight y minus 4 right parenthesis squared end fraction equals 0
solve space to space get space locus comma space also space straight x squared plus left parenthesis straight y minus 4 right parenthesis squared not equal to 0
Answered by Expert 8th December 2017, 5:17 PM
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