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

The complex number 4 + 2i on the complex plane has coordinates (4,2) and the complex number 7 - 2i has coordinates (7,-2). Thus, the length of a segment in the complex plane with endpoints at 4 + 2i and 7 – 2i is

[tex]\sqrt{(4-7)^2+(2-(-2))^2}=\sqrt{(-3)^2+4^2}=\sqrt{9+16}=\sqrt{25}=5.[/tex]

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zainebamir540 zainebamir540 · Answer 2 · 2019-02-08T11:00:05+01:00

Answer:

5

Step-by-step explanation:

From question statement , we observe that

Two end points of a line segment are given we have to calculate the length of the line segment.

On complex plane,we represent 4+2i as coordinate (4,2) and 7-2i as coordinate (7,-2).

We use distance formula to calculate the length of a line segment.

length = √(x₂-x₁)²+(y₂-y₁)²

Putting given values in above formula , we get

length = √(7-4)²+(-2-2)² = √(3)²+(-4)²

length = √9+16 = √25 = 5

Hence, the length of a segment with end points at 4+2i and 7-2i is 5.