Question

Find the distance between

Answer 1

Answer: The distance between the complex numbers is approximately
`\(14.8661\)` or
`√(221)`

Explanation:

The distance between two complex numbers
`\(a + bi\) and \(c + di\)` is given by the formula:

`$$√((c - a)^2 + (d - b)^2)$$`

This formula is similar to the Euclidean distance formula in two dimensions, where
`\(a\)` and
`\(b\)` represent the x and y coordinates of the first point, and
`\(c\)` and
`\(d\)` represent the x and y coordinates of the second point.

In this case, the two complex numbers are
`\(2 + 3i\)` and
`\(-8 + 14i\)`. So,
`\(a = 2\), \(b = 3\), \(c = -8\), and \(d = 14\)`.

Substituting these values into the formula, we get:

`$$√((-8 - 2)^2 + (14 - 3)^2) = √((-10)^2 + (11)^2) = √(100 + 121) = √(221)$$`

So, the distance between
`\(2 + 3i\)` and
`\(-8 + 14i\)` is
`\(√(221)\)`, which is approximately
`\(14.8661\)` or
`√(221)`

Answer 2

Should be 50

Explanation: