Let z be a complex number such that |z|=1.
Find the maximum value of |1+z|+|1-z+z2|.
The maximum value is 45/4.
The solution was actually 13/4.
|z|=1
z=1 or -1
if z=1,
|1+1|+|1-1+1^2|=2+1=3
if z=-1,
|1-1|+|1+1+(-1)^2|=0+3=3
it can only be 3
proof:
z^2=1
|1±z|+|1±z+1|=1±z+1±z+1=3±z±z, one has the be -1 so 3
+73 
