Arithmetic is represented in a fronto-parietal network. When the complexity in multi-digit arithmetic increases, the question arises whether primarily domain-general processing demands are increased, such as working memory in the frontal cortex, or also domain-specific processing demands, such as magnitude and place-value processing in the parietal cortex. This study addressed this question using functional near-infrared spectroscopy (fNIRS) to evaluate the neural correlates of multi-digit arithmetic in a written production paradigm. During fNIRS, adults (behavior: N = 48; fNIRS: N = 46) solved three-digit addition and subtraction problems with no, 1, or 2 carry or borrow operations, reflecting task complexity. At the behavioral level, complexity was reflected by reduced performance, i.e., lower accuracy and longer reaction times. At the neural level, fNIRS results revealed main effects of complexity in the bilateral fronto-parietal network of arithmetic processing, particularly in the bilateral inferior frontal gyrus (IFG), middle frontal gyrus (MFG), intraparietal sulcus (IPS), angular gyrus (AG), and supramarginal gyrus (SMG). Working memory differentially buffered complexity effects: larger verbal memory was linked to smaller accuracy costs and less frontal recruitment, whereas larger visuospatial memory was linked to less parietal recruitment. Together, these results show that the difficulty of multi-digit arithmetic relies on the bilateral fronto-parietal network, reflecting the joint contribution of domain-general and domain-specific processes.