Complementarity in CES Production Function
Total investment in terms of how much capital is augmented, is always $I = I_{b} + I_{h}$.  

$(I_{b}^K + I_{h}^K)^{\frac{1}{K}}$ is equal to the amount of the intermediate good $Y$ that we need to allocate for investment. And given the formulation and when $K&gt;1$ we see that we economize on the amount of the intermediate good $Y$,

$$Y_I = (I_{b}^K + I_{h}^K)^{\frac{1}{K}} &lt; I_{b} + I_{h} = I$$

Further, if we split investments equally, we achieve the maximum possible economy (i.e. the minimum $Y$ required for given total $I$ to be achieved).

So inherently, the formulation "pushes us" to keep the two investment levels close, because the further apart they are (for given total $I$), the more $Y$ we will require, reducing consumption. This "closeness of levels" is what the author refers to as "complementarity" (perhaps confusingly, if one has the micro/demand-production theory meaning of the term in mind).

Fisher, J. D. (1997). Relative prices, complementarities and comovement among components of aggregate expenditures. Journal of Monetary Economics, 39(3), 449-474.