  In the present paper we extend the concepts of multiplicative de- rivative
and integral to complex-valued functions of complex variable. Some drawbacks,
arising with these concepts in the real case, are explained satis- factorily.
Properties of complex multiplicative derivatives and integrals are studied. In
particular, the fundamental theorem of complex multiplicative calculus,
relating these concepts, is proved. It is shown that complex multi- plicative
calculus is not just another realization of the ordinary calculus. In
particular, the Cauchy formula of complex calculus disappears in multiplicative
complex calculus.
