Question

What is the length of a segment in the complex plane with endpoints at 4 + 2i and 7 – 2i?

Answer 1

just subrtact and add then you will get 5i

Answer 2

5

Explanation:

A little trick: the imaginary part (
`i`) in the coordinates of complex numbers act same as the y-coordinate in a rectangular plane.

So we want the distance between the coordinate points (4,2) and (7,-2).

How do we get the distance between 2 points? We use the distance formula.

Distance Formula =
`√((y_2-y_1)^2+(x_2-x_1)^2)`

Where
`(x_1,y_1)=(4,2)` and
`(x_2,y_2)=(7,-2)`

Let's solve for distance:

`√((-2-2)^2+(7-4)^2)\\ =√((-4)^2+(3)^2) \\=√(16+9) \\=√(25) \\=5`

Hence, the length of the segment in the complex plane with endpoints at 4 + 2i and 7 – 2i is 5.