We consider a (4+D)–dimensional Friedmann–Robertson–Walker type universe having complex scale factor R + iRI, where R is the scale factor corresponding to the usual 4–dimensional Universe while iRI is that of D–dimensional space. It is then compared with (4+D)–dimensional Kaluza–Klein Cosmology having two scale factors R and a(= iRI). It is shown that the rate of compactification of higher dimension depends on extra dimension ‘D’. The Wheeler–DeWitt equation is constructed and general solution is obtained. It is found that for D = 6 (i.e. in 10 dimension), the Wheeler–DeWitt equation is symmetric under the exchange of RI« R.