In the complex plane, what is the length of the diagonal of the square with vertices 4, 3+5i, -2+4i, and -1-i?

Also: I don't really get how to do this problem visually, because these points don't have a y coordinate

helloimnewperson May 14, 2019

#1**+1 **

We can just label the points as (4, 0) (3,5) (-2, 4) and (-1, -1)

The distance between (3, 5) and (-1, -1) will be one diagonal

So....the distance is

sqrt [ (-1-3)^2 + ( (-1-5)^2 ] = sqrt ( (-4)^2 + (-6)^2 ] = sqrt [ 16 + 36 ]= sqrt [52 ] =

sqrt(4) * sqrt(13) = 2sqrt (13) units

CPhill May 14, 2019