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Sir pls solve the following.
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Asked by rsudipto | 29 Dec, 2018, 11:46: AM
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begin mathsize 12px style Z space equals space x plus i y open vertical bar fraction numerator z minus 5 i over denominator z plus 5 i end fraction close vertical bar space equals space open vertical bar fraction numerator x plus i open parentheses y minus 5 close parentheses over denominator x plus i open parentheses y plus 5 close parentheses end fraction close vertical bar space equals space open vertical bar fraction numerator x plus i open parentheses y minus 5 close parentheses over denominator x plus i open parentheses y plus 5 close parentheses end fraction space cross times space fraction numerator x minus i open parentheses y plus 5 close parentheses over denominator x minus i open parentheses y plus 5 close parentheses end fraction close vertical bar space equals space fraction numerator 1 over denominator x squared plus open parentheses y plus 5 close parentheses squared end fraction open vertical bar x squared plus left parenthesis y squared minus 25 right parenthesis space minus space i left parenthesis 10 x right parenthesis close vertical bar space equals space space fraction numerator 1 over denominator x squared plus open parentheses y plus 5 close parentheses squared end fraction space square root of open square brackets open parentheses x squared plus open parentheses y squared minus 25 close parentheses close parentheses squared plus 100 x squared close square brackets end root H e n c e space i f space space open vertical bar fraction numerator z minus 5 i over denominator z plus 5 i end fraction close vertical bar space equals 1 space comma space t h e n space fraction numerator 1 over denominator x squared plus open parentheses y plus 5 close parentheses squared end fraction space square root of open square brackets open parentheses x squared plus open parentheses y squared minus 25 close parentheses close parentheses squared plus 100 x squared close square brackets end root space space equals space 1 space................. left parenthesis 1 right parenthesis end style
 
if z lies on x-axis means, y= 0
Let us check the equation (1) for the condition y=0,  begin mathsize 12px style fraction numerator 1 over denominator x squared plus 25 end fraction square root of open parentheses x to the power of 4 minus 50 x squared plus 625 plus 100 x squared close parentheses end root space equals space fraction numerator begin display style 1 end style over denominator begin display style x squared plus 25 end style end fraction square root of open parentheses x to the power of 4 plus 50 x squared plus 625 close parentheses end root space equals space space fraction numerator begin display style x squared plus 25 end style over denominator begin display style x squared plus 25 end style end fraction space equals space 1 end style
Hence Z lies on x-axis
Answered by Thiyagarajan K | 29 Dec, 2018, 01:14: PM

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