To find the distance between two complex numbers in the complex plane, we can treat them as points in a two-dimensional space. The complex number 1 + 3i corresponds to the point (1, 3) and 2 + 4i corresponds to the point (2, 4).
We can use the distance formula, which is derived from the Pythagorean theorem. The distance d between two points (x₁, y₁) and (x₂, y₂) is given by:
d = sqrt((x₂ - x₁)² + (y₂ - y₁)²)In this case:
- (x₁, y₁) = (1, 3)
- (x₂, y₂) = (2, 4)
Now, substituting these values into the distance formula:
d = sqrt((2 - 1)² + (4 - 3)²)This simplifies to:
d = sqrt((1)² + (1)²)
= sqrt(1 + 1)
= sqrt(2)Thus, the distance between the complex numbers 1 + 3i and 2 + 4i in the complex plane is √2 or approximately 1.41.