Question

Find the distance between the points below.
4 + 3i and 9 – 9i

Answer 1

13 units.

Explanation:

The complex numbers can be thought of as points on the xy plane, where their real part (denoted Re(z)), and their imaginary part (Im(z)) serve as the coordinates for these numbers, and since we know how to calculate distances between points we can calculate the distance between these numbers:

Formula:
`d(z_1, z_2) = √((\Re(z_2) - \Re(z_1))^2 + (\Im(z_2) - \Im(z_1))^2){} =>\\d(4+3i, 9 - 9i) = √((9-4)^2 + (-9-3)^2) = √(5^2 + 12^2) = √(169) = √(13^2) = 13`