complex numbers - What did I do wrong? 1 = √1 = √(-1)(-1) = √(-1) √(-1) = i.i = i² = -1

I'm a simple man living my life and enjoying mathematics now and then. Today during lunch my friend asked me about complex numbers and $i$. I told him what I knew and we went back to work.

After work I decided to read up on complex numbers and I somehow ended up with this equation:

$$1 = \sqrt 1 = \sqrt{(-1)(-1)} = \sqrt{(-1)} \ \sqrt{(-1)} = i \cdot i = i² = -1$$

Somehow I got that $1 = -1.$ I can't see a contradiction. Did I just break math? What happened? Where is my mistake?