Question

Find the distance d between z_(1)=(8+3i) and z_(2)=(5-7i). Express your answer

Answer 1

The distance between z1=(8+3i) and z2=(5-7i) is approximately sqrt(109).

Step-by-step explanation:

To find the distance between two complex numbers, we use the distance formula:

d = |z2 - z1|

Let's plug in the given values for z1 and z2:

d = |(5-7i) - (8+3i)|

Subtract the real parts and the imaginary parts:

d = |(5-8) + (-7-3)i|

d = |-3 - 10i|

Use the Pythagorean theorem to find the magnitude:

d = sqrt((-3)^2 + (-10)^2)

d = sqrt(9 + 100)

d = sqrt(109)

So, the distance between z1 and z2 is approximately sqrt(109).