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Studying for a test: IIR filter question

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Hmemo

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hi,
I'm studying for a test, and found this question in one of the previous exams but there is no solution and I was not able to solve it myself.
It would be very helpful if anybody could help =]

The question:
if h(t) is an analog IIR filter, with the poles λ_1 = -1, λ_2 = -1+i, λ_3 = -1-i and no zeros. and h[n] is a digital IIR filter with poles which defined by e^λ_i and no zeros. is h[n] a high pass filter?

Thanks
 

Just guessing, but I thought a high-pass HAS to have a zero. I'd be interested to know the right answer.
 

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