What is the distance between 4-i and -2+3i?

If you're working with complex numbers, then I'm sure you're comfortable with plotting them on a complex-plane ... real part of the number along the x-axis, and imaginary part of the number along the y-axis.

When you look at it that way, your two points are simply two points on the x-y plane:

           4 - i    ===>  (4, -1)

         -2 + 3i  ===>  (-2, 3) .

The distance between them is

                       D  =  √ (difference in 'x')² + (difference in 'y')²

                           =  √  (6)² + (4)²

                           =  √ (36 + 16)

                           =   √ (52)

                           =      7.211  (rounded)   

Use basic math on google