please show all work n Please Explain Evaluate the function

please show all work!!! n Please Explain!

Evaluate the function f(z) = log_e |z| + iArg(z) at the points z = 3, z = -3i, z = -2 - 2i.

z=3+0i

|z|=(9)^1/2=3

Arg z =0 as x=3>0 and y=0

f(z)=loge 3

z=-3i

|-3I|=(-3)^2)^1/2=3

Argz =-pi/2 as x=0,y<0

f(z)=loge3-pi/2

z=-2-2i

|z|= (-2^2+-2^2)^1/2=(8)^1/2

Argz= -pi - tan^-1(y/x)= -pi- tan^-1(1)

= -pi-pi/4=-5pi/4.

f(z)=loge8^1/2+i(-5pi)/4