Question

Find the distance using the modulus of the difference between z1 = -8 + 3i and z2 = 7 - 4i.

Answer 1

`d = 16.55`

Explanation:

Given

`z_1 = -8 + 3i`

`z_2 = 7 - 4i`

Required

The distance between them

First, calculate the difference (d) between z1 and z2

`d = z_1 - z_2`

`d = -8 + 3i - [7 - 4i]`

Open bracket

`d = -8 + 3i - 7 + 4i`

Collect like terms

`d = -8 - 7+ 3i + 4i`

`d = -15+ 7i`

Using modulus, we have:

`d = √(R^2 + I^2)`

Where

R = Real Part = -15

I = Imaginary Part = 7

So, we have:

`d = √((-15)^2 + 7^2)`

`d = √(225 + 49)`

`d = √(274)`

`d = 16.55`