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Consider the equationof line abarz + baraz + b=0, whereb is arealparameterand a isfixed non-zero complex number. The locus of mid-point of thelineintercepted between real and imaginary axis is givenby |
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Answer» `az- BAR(az) =0` Let thePQbe thesegement intercept between axes. Forintercept on real axis `Z_(R)`. `Z =barz` `rArr Z_(R)(a+ bara) + b =0` ` rArr Z_(R) = (-b)/(a + bara)` For interceptonimaginary `Z_(1)` `z +barz = 0` `rArr Z_(1)(bara - a) + b=0` `rArr Z_(1)= (b)/(a+bara)` For mid-point, `z= (Z_(R) + Z_(I))/(2)` `rArr z =(-b)/(2)[(1)/(bara+a)+(1)/(bara +a)]` `z= (barab)/((a + bara)(a-bara))` `rArr z = (barab)/(a^(2) -(a)^(2))` `(z[a^(2)-(a)^(2)])/(bara) = barz((bara)^(2) - (a)^(2))/(a)` `rArr az + bar(az) =0` |
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