Let $z_1$ and $z_2$ be complex numbers such that $\frac{z_2}{z_1}$ is pure imaginary and $2z_1 \neq 7z_2.$  Compute
\[\left| \frac{2z_1 + 7z_2}{2z_1 - 7z_2} \right|.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $z_1$ and $z_2$ be complex numbers such that $\frac{z_2}{z_1}$ is pure imaginary and $2z_1 \neq 7z_2.$  Compute
\[\left| \frac{2z_1 + 7z_2}{2z_1 - 7z_2} \right|.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
1
Let $z_1$ and $z_2$ be complex numbers such that $\frac{z_2}{z_1}$ is pure imaginary and $2z_1 \neq 7z_2.$  Compute
\[\left| \frac{2z_1 + 7z_2}{2z_1 - 7z_2} \right|.\]
train