A complex point of the form a + 3i has a distance of 29 units from –9 + 24i. What is the value of a?

The distance between two complex numbers is the distance between their coordinate pairs. Here, the imaginary parts differ by 3 − 24 = −21, so the real-part difference must satisfy (a − (−9))² + (−21)² = 29². This gives (a + 9)² = 400, so a + 9 = 20 or −20; among the choices, a = 11. The correct choice is 11.

AI-written and checked against the verified answer.