Question

If \(z_1 = x_1 + iy_1 \) and \(z_2 = x_2 + iy_2\) are two complex points, then show that the distance between them is \(|z_1 - z_2| \)

Answer 1

z1-z2=(x1-x2)+i(y1-y2)
|z1-z2|=sqrt((x1-x2)^2+(y1-y2)^2)
this is the same as the distance between the two points z1 and z2

Answer 2

distance between them..\[\sqrt{(x2-x1)^{^2 }+(y2-y1)^{^{2}}}\]

and z2 -z1 =( x2-x1 )+i(y2-y1)
I z2-z1I =
\[\sqrt{(x2-x1)^{^2 }+(y2-y1)^{^{2}}}\]