Question

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

Answer 1

Answer:

$d = 16.55$

Step-by-step 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:

$d = \sqrt{R^2 + I^2}$

Where

R = Real Part = -15

I = Imaginary Part = 7

So, we have:

$d = \sqrt{(-15)^2 + 7^2}$

$d = \sqrt{225 + 49}$

$d = \sqrt{274}$

$d = 16.55$