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Question: How many roots are there in this equation?

Question:How many roots are there in this equation?

minhthien2016 370 Maple
complex solve
June 29 2018
3

I want to find all complex numbers such that 
abs(z)*(z-4-I)+2*I = (5-I)*z.
I tried solve(abs(z)*(z-4-I)+2*I = (5-I)*z, z)
and got the answer is z = -1.
This is a question in a test with multiple choice. The key of question is three numbers.

Is my commant wrong? Where is wrong?
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