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JEE Main Math Class 11 Complex Numbers and Quadratic Equations Part 1 Questions
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© examsnet.com
Question : 5
Total: 100
Let
α
and
β
be two roots of the equation
x
2
+
2
x
+
2
=
0
,
then
α
15
+
β
15
is equal to:
[Jan. 9, 2019 (I)]
-256
512
-512
256
Validate
Solution:
Consider the equation
x
2
+
2
x
+
2
=
0
x
=
−
2
±
√
4
−
8
2
=
−
1
±
i
Let
α
=
−
1
+
i
,
β
=
−
1
−
i
α
15
+
β
15
=
(
−
1
+
i
)
15
+
(
−
1
−
i
)
15
=
(
√
2
e
i
3
π
4
)
15
+
(
√
2
e
−
i
3
π
4
)
15
=
(
√
2
)
15
[
e
i
45
π
4
+
e
−
i
45
π
4
]
=
(
√
2
)
15
⋅
2
cos
45
π
4
=
(
√
2
)
15
⋅
2
cos
3
π
4
=
−
2
√
2
(
√
2
)
15
=
−
2
(
√
2
)
14
=
−
256
© examsnet.com
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