In the set of complex numbers let $z_{1}=\operatorname{cis}\left(\dfrac{\pi}{7}\right)$ and $z_{2}=2+i$. Prove that $|z_{1}+z_{2}|^2=6+4\cos\left(\frac{\pi}{7}\right)+2\sin\left(\frac{\pi}{7}\right)\;.$
I thought to convert $z_{1}$ into algebric form, because I know how to sum two complex numbers in algebric form. But the argument is not a special angle, easy to find the trig value. Other issue, are the "brackets": I don't know what they mean. Absolute value? Modulus?
Can you explain to me how to do this? Thanks