The complex multiplier is the multiplier principle in Keynesian economics (formulated by John Maynard Keynes).
The simplistic multiplier that is the reciprocal of the marginal propensity to save is a special case used for illustrative purposes only.
The multiplier applies to any change in autonomous expenditure, in other words, an externally induced change in consumption, investment, government expenditure or net exports.
Each of these operates to increase or reduce the equilibrium level of income in the economy.
The size of the multiplier should take account of all leakages from the circular flow of income and expenditure occurring in all sectors.