Why is |z| = 1 a circle of radius one? (FP2)

So, basically |z| = 1 is equal to the set containing all complex numbers where their magnitude is equal to one. Also, by unraveling the definition of |z| we get that (x²+y²)^1/2=1 which is the same as x²+y²=1 which we can identify as the circle with centred at (0,0) and radius 1.