1. Find the modulus

I'm not sure how to deal with this problem (see attachment) when they have a treated as a real number. I know I have to use the modulus theorem but I think it may just be the algebra involved with leaving a as a real number that is giving me the problem. I have attached my working if it's not clear what I mean. (see attachment)

2. You might note that $\left| {2a - i} \right| = \left| {2a + i} \right| = \sqrt {4a^2 + 1} \;\& \;\left| {a + i} \right|^4 = \left( {a^2 + 1} \right)^2$.
And so $\left| z \right| = \frac{{\left( {a^2 + 1} \right)^2 }}