can any one help me understand euler's formula :

exp(j.theta)=cos(theta)+j.sin(theta)

i don't want the mathematical proof......i want the physical meaning given that

cos(theta)+j.sin(theta) ............is a rotating vector of magnitude 1
j : is a 90 degree shift operator
exp : euler constant.........just a number

so how a number raised to the power of (a 90 degree shift operator) gives a rotating vector !!!!!!!!


thank u very much