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

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06-08-2017
Mathematics

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

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jdoe0001 jdoe0001 · Answer 1 · 2017-08-06T21:56:25+02:00

[tex]\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}[/tex]