We derive a measure of the relatedness between economic activities based on weighted correlations of local employment shares, and use this measure to estimate city and activity complexity. Our approach extends discrete measures used in previous studies by recognising the extent of activities' local over-representation and by adjusting for differences in signal quality between geographic areas with different sizes. We examine the contribution of relatedness and complexity to urban employment growth, using 1981-2013 census data from New Zealand. Complex activities experienced faster employment growth during our period of study, especially in complex cities. However, this growth was not significantly stronger in cities more dense with related activities. Relatedness and complexity appear to be most relevant for analysing how large, complex cities grow, and are less informative for understanding employment dynamics in small, less complex cities.