Factorising this polynomial over C

Hi there

I'm having trouble getting this problem out.

I have to factorise this over c.

$\displaystyle 4z^2 - 4z + 17$

My answer is:

$\displaystyle z^2 - z + \frac{17}{4}$

$\displaystyle (z^2 - z + \frac{1}{4}) + \frac{17}{4} - \frac{1}{4}$

$\displaystyle (z - \frac{1}{2})^2 + \frac{16}{4}$

$\displaystyle (z - \frac{1}{2})^2 + 4$

$\displaystyle (z - \frac{1}{2})^2 - (2i)^2$

$\displaystyle (z - \frac{1}{2} - 2i)(z - \frac{1}{2} + 2i)$

However, the answer in the book is this:

$\displaystyle (2z - 1 + 4i)(2z - 1 - 4i)$

Is this the same as what I had?

Also, have I put this complex number question in the right forum? What section should a question like this go?