To find the distance between two points in the complex plane, we can use the distance formula derived from the Pythagorean theorem. The points given are 1 + 3i and 2 + 4i.
First, we can represent these points as complex numbers: let z1 = 1 + 3i and z2 = 2 + 4i.
The distance d between two complex numbers z1 and z2 is calculated as follows:
d = |z2 – z1|
Now, we first need to calculate z2 – z1:
- z2 – z1 = (2 + 4i) – (1 + 3i) = (2 – 1) + (4i – 3i) = 1 + i
Next, we find the magnitude of this result to determine the distance:
|1 + i| = √(1² + 1²) = √(1 + 1) = √2
Thus, the distance between the two points 1 + 3i and 2 + 4i in the complex plane is √2.