<h2>
Answer:</h2>
The value of b is: 4 and -66
<h2>
Step-by-step explanation:</h2>
We are given distance between two points i.e. 25+bi and 13-31i as: 37 units.
We know that the point 25+bi is given in coordinate plane as: (25,b)
and 13-31i is given in coordinate plane as: (13,-31)
Since, any complex number is expressed in the form z=x+iy
Now we know that the distance between two points (a,b) and (c,d) is given by:
Here we have:
Distance=37 units.
(a,b)=(25,b) and (c,d)=(13,-31)
Hence, we have:
Now on squaring both side we obtain:
on taking square root both side we obtain:
Hence, the value of b is: 4 and -66