On l_p-Complex Numbers

Dispensing with the common property of distributivity and replacing classical trigonometric functions with their $l_p$ -counterparts in Euler’s trigonometric representation of complex numbers, classes of $l_p$ -complex numbers are introduced and some of their basic properties are proved. The collection of all points that leave the $l_p$ -absolute value of each $l_p$ -complex number invariant under $l_p$ -complex numbers multiplication is shown to be a group of elements that have $l_p$ -absolute value one but not the symmetry group.