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Mathematics
Mathematics
Problem
Let the vertices
A
(
a
)
A(a)
A
(
a
)
,
B
(
b
)
B(b)
B
(
b
)
,
C
(
c
)
C(c)
C
(
c
)
,
D
(
d
)
D(d)
D
(
d
)
,
E
(
e
)
E(e)
E
(
e
)
,
F
(
f
)
F(f)
F
(
f
)
taken in anticlockwise manner form a regular hexagon in the argand plane. If
a
=
−
2
a = -2
a
=
−
2
and
c
=
1
−
3
i
c = 1 - \sqrt{3}i
c
=
1
−
3
i
, where
i
=
−
1
i = \sqrt{-1}
i
=
−
1
, then the value of
d
2
−
a
2
−
b
2
−
c
2
−
e
2
−
f
2
d^2 - a^2 - b^2 - c^2 - e^2 - f^2
d
2
−
a
2
−
b
2
−
c
2
−
e
2
−
f
2
is equal to
−
−
−
- - -
−
−
−
.
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