Question

Find the distance between 4+3i and 6-2i

Answer 1

$\bf \stackrel{\textit{over the imaginary plane}}{4+3i\implies (4,3)\qquad \qquad 6-2i\implies (6,-2)} \\\\\\ ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ 4 &,& 3~) % (c,d) &&(~ 6 &,& -2~) \end{array}~~~ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(6-4)^2+(-2-3)^2}\implies d=\sqrt{2^2+(-5)^2}\implies d=\sqrt{29}$