Answer:
u − v = 〈s − a, t − b〉
u − v = √(s − a)2 + (t − b)2
EXAMPLE 1 Finding the Distance Between Points
in the Complex Plane
Find the distance between the points 2 + 3i and 5 − 2i in the complex plane.
Solution
Let a + bi = 2 + 3i and s + ti = 5 − 2i. The difference between the complex
numbers is
(5 − 2i) − (2 + 3i) = (5 − 2) + (−2 − 3)i = 3 − 5i.
The distance is
d = √32 + (−5)2 = √34 ≈ 5.83 units
Step-by-step explanation:
The distance between (2 + 2i) and (6 + 5i) is 5
We have to determine, the distance between (2 + 2i) and (6 + 5i).
The distance between a given point is found by using the distance formula given below.
[tex]Distance = \sqrt{(x_2-x_1 )^2 + (y_2-y_1)^2}[/tex]
In the complex Plane the distance between the points (2 + 2i) and (6+ 5i) in the complex plane.
The distance between (2 + 2i) and (6 + 5i) is,
[tex]= (2-6,\ 2i-5i)\\\\= (4, -3i)[/tex]
Therefore, The distance between the complex point is,
[tex]Distance = \sqrt{(2-6 )^2 + (2i-5i)^2}\\\\Distance = \sqrt{(-4 )^2 + (-3i)^2}\\\\Distance = \sqrt{16 + 9i^2}\\\\Distance = \sqrt{16+9}\\\\Distance = \sqrt{25}\\\\Distance = 5[/tex]
Hence, The required distance between (2 + 2i) and (6 + 5i) is 5.
To know more about Complex roots click the link given below.
https://brainly.com/question/13264377
