# Complex Quadratic Residues

Complex Quadratic Residues

The squares of the numbers from 0 to 14 are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196.

Those squares are 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1. The numbers 0, 1, 4, 6, 9, 10 are the possible quadratic residues . The missing numbers 2, 3, 5, 7, 8, 11, 12, 13, 14 are the nonresidues.

(mod15)

(mod15)

What happens with a complex modulus? This Demonstration plots complex quadratic residues. The largest value needed to find all nonzero residues is .

(moda+bi)

ceiling((+)2)

2

a

2

b