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

Answer:

5

Step-by-step 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 = $\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

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

Let's solve for distance:

$\sqrt{(-2-2)^2+(7-4)^2}\\ =\sqrt{(-4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5$

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