Distance between Two Complex Numbers

Question

4+3i

and

6-2i

Find the distance between them.

Answer 1

d^2 = sum of the change in x coordinates squared + the sum of the change in y coordinates

think of the two points as (4,3i) and (6,-2i)

d^2 = (6-4)^ + (-2i-3i)^2 = 4 + -25 = 29

distance = sqr29 = about 5.4

Answer 2

To get distance between these numbers we have to find modulus of their difference:

z = z₁ - z₂ = (4 + 3i) - (6 - 2i) = - 2 + 5i.

So, distance d = abs(- 2 + 5i) = √((- 2)² + 5²) = √(29)