# FIR Filter 3dB Frequency

I am new to signal processing and I want to calculate the 3 dB - cut off frequency of this FIR filter, which has the following transfer function:

For the evaluation i need to replace the z with and set the squared magnitude equal to 1/2.

But the problem is when I want to solve this for omega zero is the result. My question is what am I doing wrong here, or is something missing ?

1. The expression $$\displaystyle\frac{1+z^{-1}}{2}$$ is the transfer function $$H(z)$$, NOT its magnitude $$|H(z)|$$.
2. Consequently, the expression $$\displaystyle \frac{1+e^{-j\Omega}}{2}$$ is the complex frequency response $$H(e^{j\Omega})$$, not its magnitude.
So now you have to compute the squared magnitude of $$H(e^{j\Omega})$$ and set it equal to $$\frac12$$. This is a basic exercise in complex numbers, so I trust that you can take it from here.
$$\cos(\Omega_c)=0\tag{1}$$
which certainly does not imply that $$\Omega_c=0$$. What is it that it does imply?