Answer:
[tex]d = 16.55[/tex]
Step-by-step explanation:
Given
[tex]z_1 = -8 + 3i[/tex]
[tex]z_2 = 7 - 4i[/tex]
Required
The distance between them
First, calculate the difference (d) between z1 and z2
[tex]d = z_1 - z_2[/tex]
[tex]d = -8 + 3i - [7 - 4i][/tex]
Open bracket
[tex]d = -8 + 3i - 7 + 4i[/tex]
Collect like terms
[tex]d = -8 - 7+ 3i + 4i[/tex]
[tex]d = -15+ 7i[/tex]
Using modulus, we have:
[tex]d = \sqrt{R^2 + I^2}[/tex]
Where
R = Real Part = -15
I = Imaginary Part = 7
So, we have:
[tex]d = \sqrt{(-15)^2 + 7^2}[/tex]
[tex]d = \sqrt{225 + 49}[/tex]
[tex]d = \sqrt{274}[/tex]
[tex]d = 16.55[/tex]
