Test and analysis: It can be obtained by using the operation law of complex numbers and periodicity i4= 1.

analyse

∵i4= 1,∴i2009=(i4)502？ i=i，

∴ complex number z = (1+I) 2+i2009 =1+2i+I2+I = 3i,

So the imaginary part of the complex number z is 3.

So choose D.