Find the complex number $z$ so that $z + |z| = 2 + 8i.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the complex number $z$ so that $z + |z| = 2 + 8i.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
-15 + 8i
Find the complex number $z$ so that $z + |z| = 2 + 8i.$
train