Question

Find the distance between -3+2i and 5+i

Answer 1

The distance between the complex numbers -3+2i and 5+i is calculated as the square root of 65 by using the distance formula for complex numbers, similar to the Pythagorean theorem.

Step-by-step explanation:

The distance between two complex numbers, -3+2i and 5+i, is found using the distance formula for complex numbers, which is similar to the Pythagorean theorem and calculates the modulus of the difference between the two numbers. To compute this, we take the difference between the two complex numbers, find the real and imaginary parts of the result, and then apply the distance formula:

1. Subtract the second complex number from the first: (-3 + 2i) - (5 + i) = (-3 - 5) + (2i - i) = -8 + i.
2. Calculate the square of the real part and the square of the imaginary part: (-8)^2 + (1)^2 = 64 + 1 = 65.
3. Take the square root of the sum to find the distance: \(\sqrt{65}\).

The distance between the complex numbers -3+2i and 5+i is \(\sqrt{65}\).