Question

What is the distance between z1 = 5 - 2i and z2 = 8 + i?

2sqrt3
13.3
3sqrt2
18"

Answer 1

The distance between the complex numbers z1 = 5 - 2i and z2 = 8 + i is calculated using the distance formula for complex numbers, yielding a result of 3√2.

Step-by-step explanation:

The distance between two complex numbers z1 and z2 is found by treating them as points in the complex plane and using the distance formula which is analogous to the Pythagorean theorem. The distance d between z1 = 5 - 2i and z2 = 8 + i is calculated as follows:

• First, find the difference between the numbers: (8 - 5) + (1 - (-2))i = 3 + 3i.
• Then calculate the magnitude of the difference: |3 + 3i| which is √(3² + 3²) = √(9 + 9) = √18.
• The magnitude, which represents the distance, simplifies to 3√2.

Therefore, the distance between z1 and z2 is 3√2, which matches one of the given options.