Mathematics: What is the distance between (-5 -4i) and (-4+ 2i) on the complex plane?

What is the distance between (-5 -4i) and (-4+ - id54422909390, tiwaribianca475

Ответ:

emilyf05

05.01.2022

$\bf \begin{array}{clclll}
-5-4i&& -4+2i\\
\uparrow &&\uparrow \\
(-5,-4)&&(-4,2)
\end{array}\\\\
-------------------------------\\\\
\textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ -5}}\quad ,&{{ 4}})\quad 
% (c,d)
&({{ -4}}\quad ,&{{ 2}})
\end{array}\qquad 
% distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
d=\sqrt{[-4-(-5)]^2+[2-(-4)]^2}\implies d=\sqrt{(-4+5)^2+(2+4)^2}
\\\\\\
d=\sqrt{1^2+6^2}\implies d=\sqrt{37}$