Suppose z = 2(cos@ + isin@)
Conjugate z = 2(cos@ - isin@), so just reflected across the x-axis.
-z/2 would be reflected across the x and the y axis where the modulus is halved (so now 2)
1/z - it is reflected across the x-axis and the modulus is now 1/4 (shrinked to 25% original)
sqrt(z) -...