A sequence of complex numbers converges to a limit c if, in the epsilon-delta sense, the modulus of the difference between terms and c shrinks below any epsilon for sufficiently large index — a direct analogue of real-sequence convergence with modulus replacing absolute value. This belongs to complex analysis and connects to real analysis via a key theorem: a complex sequence converges if and only if both its real-part and imaginary-part sequences converge (to the real and imaginary parts of the limit, respectively), which lets many real-sequence results (boundedness of convergent sequences, the Cauchy criterion) transfer directly to the complex setting, while others (monotonicity, the monotone sequence theorem) remain meaningful only for real sequences since the complex numbers lack a canonical ordering.
A sequence of complex numbers converges to a limit c if, in the epsilon-delta sense, the modulus of the difference between terms and c shrinks below any epsilon for sufficiently large index — a direc…