Question

Find the distance between
2-3i
And
9+21i

Answer 1

2 - 3i is just another of writing (2, -3) in the cartesian plane, the 2-3i however is using the "imaginary axis" for the imaginary plane, is all however the imaginary axis is simply the equivalent of the y-axis. Likewise 9+21i is just (9,21), so let's just use the distance formula.

`\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{9}~,~\stackrel{y_2}{21})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([9-2]^2+[21-(-3)]^2)\implies d=√((9-2)^2+(21+3)^2) \\\\\\ d=√(7^2+24^2)\implies d=√(49+576)\implies d=√(625)\implies d=25`