angelo3892019
Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

Sagot :

MrRoyal

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]

We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.