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

Treat the complex numbers as points with coordinates: 25 + bi is (25, b), and 13 − 31i is (13, −31). Their horizontal separation is 25 − 13 = 12, so the distance formula gives 12² + (b + 31)² = 37². Thus (b + 31)² = 1225, so b + 31 = 35 or −35; the resulting values are b = 4 or b = −66. Of the choices, only 4 is listed.

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