Question

Find the distance between the complex numbers in the complex plane.7i, 4 − 3i

Answer 1

Given:

There are given two complex number is:

$7i,4-3i$

Explanation:

According to the question:

We need to find the value of the distance between two complex numbers.

Then,

From the given complex number:

$7\imaginaryI,4-3\imaginaryI$

That means, the point is:

$(0,7),and,(4,-3)$

Now,

From the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Where,

$x_1=0,y_1=7,x_2=4,y_2=-3$

Then,

$\begin{gathered} d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt{(4-0)^2+(-3-7)^2} \\ d=\sqrt{(4)^2+(-10)^2} \end{gathered}$

Then,

$\begin{gathered} d=\sqrt{(4)^2+(-10)^2} \\ d=\sqrt{16+100} \\ d=\sqrt{116} \end{gathered}$

Final answer:

Hence, the value of the distance is shown below:

$d=\sqrt{116}$