What is the distance between 1 + 3i and 2 - 4i in the complex plane?

Solution:

Given, the complex vectors are 1 + 3i and 2 - 4i.

The complex vectors can be written as (1,3) and (2,-4) on the coordinate plane.

We have to find the distance between the two vectors.

Using distance formula,

\(D = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

Distance, D = \(\sqrt{(2-1)^{2}+(-4-3)^{2}}\)

= \(\sqrt{(1)^{2}+(-7)^{2}}\)

= \(\sqrt{(1+49)}\)

= \(\sqrt{50}\)

Therefore, the distance between the given vectors is \(\sqrt{50}\) units.

What is the distance between 1 + 3i and 2 - 4i in the complex plane?

Summary:

The distance between 1 + 3i and 2 - 4i in the complex plane is \(\sqrt{50}\) units.