jmc

Question

Amerigo Vespucci has a map of America drawn on the complex plane. The map does not distort distances. Los Angeles corresponds to 0 on this complex plane, and Boston corresponds to 2600i. Meanwhile, Knoxville corresponds to the point 780+1040i. With these city-point correspondences, how far is it from Knoxville to Los Angeles on this complex plane?

Accepted Answer

Note that 780= 310 2600, and 1040=410 2600. Thus, geometrically, the distance from Los Angeles to Knoxville forms a 3-4-5 right triangle, with hypotenuse of length 510 2600=1300. Since magnitude of a number is defined to be the distance from the origin of that number, 1300 is our answer.