Question

Find the distance between the complex numbers. z1=9-9i, z2=10-9i

Answer 1

$\bf z_1=\stackrel{a}{9}\stackrel{b}{-9}i\implies (9~,~-9)\qquad \qquad \qquad z_2=\stackrel{a}{10}\stackrel{b}{-9}i\implies (10~,~-9)\\\\ -------------------------------\\\\ ~~~~~~~~~~~~\textit{distance between 2 points}\\ \quad$

$\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~{{ 9}} &,&{{ -9}}~) % (c,d) &&(~{{ 10}} &,&{{ -9}}~) \end{array}\quad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ d=\sqrt{[10-9]^2+[-9-(-9)]^2}\implies d=\sqrt{(10-9)^2+(-9+9)^2} \\\\\\ d=\sqrt{1^2+0}\implies d=\sqrt{1}\implies d=1$