Question

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

Answer 1

a = 11 or a = -29

Explanation:

A: a+3i B: -9+24i AB = 29

AB² = (a - -9)² + (3 - 24)² = (a + 9)² + (-21)²

AB² = a² + 18a + 81 + 441 = 29² = 841

a² + 18a -319 = 0

a = (-18 ± √18²-4*1*(-319)) / 2 = (-18 ± √1600) / 2 = (-18 ± 40)/2

a = 11 or a = -29