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Mathematics
Problem
If
a
,
b
,
c
,
a
1
,
b
1
a, b, c, a_1, b_1
a
,
b
,
c
,
a
1
,
b
1
and
c
1
c_1
c
1
are non-zero complex numbers satisfying
a
a
1
+
b
b
1
+
c
c
1
=
1
+
i
\frac{a}{a_1} + \frac{b}{b_1} + \frac{c}{c_1} = 1 + i
a
1
a
+
b
1
b
+
c
1
c
=
1
+
i
and
a
1
a
+
b
1
b
+
c
1
c
=
0
\frac{a_1}{a} + \frac{b_1}{b} + \frac{c_1}{c} = 0
a
a
1
+
b
b
1
+
c
c
1
=
0
, where
i
=
−
1
i = \sqrt{-1}
i
=
−
1
, the value of
a
2
a
1
2
+
b
2
b
1
2
+
c
2
c
1
2
\frac{a^2}{a_1^2} + \frac{b^2}{b_1^2} + \frac{c^2}{c_1^2}
a
1
2
a
2
+
b
1
2
b
2
+
c
1
2
c
2
is a. 2i b.
2
+
2
i
2+2i
2
+
2
i
c. 2 d. None of these
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