(c) दी गयी संख्यायें   

${z_1} = 10 + 6i,{z_2} = 4 + 6i$ एवं $z = x + iy$ हैं

$amp\left( {\frac{{z – {z_1}}}{{z – {z_2}}}} \right) = \frac{\pi }{4}$Þ $amp\left[ {\frac{{(x – 10) + i\,(y – 6)}}{{(x – 4) + i\,(y – 6)}}} \right] = \frac{\pi }{4}$

$\frac{{(x – 4)(y – 6) – (y – 6)(x – 10)}}{{(x – 4)(x – 10) + {{(y – 6)}^2}}} = 1$

$12y – {y^2} – 72 + 6y = {x^2} – 14x + 40$………$(i)$

अब  $|z – 7 – 9i|\, = |\,(x – 7) + i(y – 9)|$

$\sqrt {{{(x – 7)}^2} + {{(y – 9)}^2}} $……….$(ii)$

$(i) $ से,  $({x^2} – 14x + 49) + ({y^2} – 18y + 81) = 18$

${(x – 7)^2} + {(y – 9)^2} = 18$

या  ${[{(x – 7)^2} + {(y – 9)^2}]^{1/2}} = {[18]^{1/2}} = 3\sqrt 2 $

 $|(x – 7) + i(y – 9)| = 3\sqrt 2 $या $|z – 7 – 9i| = 3\sqrt 2 $.