In this paper, the polar representation of complex numbers is extended to complex polar intervals or sectors; detailed algorithms are derived for performing basic arithmetic operations on sectors. While multiplication and division are exactly defined, addition and subtraction are not, and we seek to minimize the pessimism introduced by these operations. Addition is studied as an optimization problem which is analytically solved. The complex interval arithmetic thus defined is illustrated with some numerical examples which show that in many applications, the polar representation is more advisable.