Let z=a+ib
Then l z l = root(a^2+b^2)
l z- 1 l = root[(a-1)^2+b^2]
l z+1 l = root[(a+1)^2+b^2]
if a is -ve then lz+1 l is min. & if a is +ve then lz-1 l is min.
CASE I: when a is -ve then
lzl^2 = lz+1l^2
a^2+b^2=a^2+2a+1+b^2
2a+1=0
a= -1/2
then z + conjugate of z = 2a
= -1
CASE II:when a is +ve then
lzl^2 = lz-1l^2
a^2+b^2=a^2-2a+1+b^2
-2a+1=0
a= 1/2
then z + conjugate of z = 2a
= 1
therefore the possible answers r (-1) & 1
Moderation Team
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