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

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

Ответ:

keigleyhannah30

15.03.2022

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

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