Algebraic form of complex number

I want to obtain the result of a definite integral as a complex number expressed in the algebraic form. I tried:

Integrate[E^z, {z, 0, 1 + I \[Pi]/4}] // ComplexExpand[#, TargetFunctions -> {Re, Im}] & 

but the result is not what I expected. How can I obtain -1+E/Sqrt[2]+I E/Sqrt[2]? Moreover, is it possible to rationalize the denominator of the fractions?