Recently two interesting conjectures on the linear complexity of binary complementary sequences of length 2nN0 were given by Karkkainen and Leppanen when those sequences are considered as periodic sequences with period 2nN0, where those sequences are constructed by successive concatenations or successive interleavings from a pair of kernel complementary sequences of length N0. Their conjectures were derived from numerical examples and suggest that those sequences have very large linear complexities. In this paper we give the exact formula of characteristic polynomials for those complementary sequences and show that their conjectures are true.