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A point of the form 25 +bi is 37 units from 13 – 31i. What is the value of b

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If we consider the positive value of b, then the value of b is 4.

What is the coordinate plane of a complex number?

A complex number in the form z = x + iy takes a coordinate plane in terms of (x,y). From the given information, we are given a distance between two points:

- 25 + bi = (25,b)
- 13-31i = (13, -31)

Now, the distance between two points can be represented by using the relation:

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

$$\mathbf{37 = \sqrt{(13-25)^2+(-31-b)^2}}$$

$$\mathbf{37 = \sqrt{(-12)^2+(31+b)^2}}$$

$$\mathbf{37 = \sqrt{144+(31+b)^2}}$$

Taking the square of both sides

1369 = 144 + (31 + b)²

1369 - 144 = (31 + b)²

1225 = (31 + b)²

(31 + b)² = (35)²

(31 + b) = ±35

b = 35 - 31 or -35 -31

b = 4 or -66