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Byju's Answer
Standard XII
Mathematics
Properties of Iota
If α and β ar...
Question
If
α
and
β
are the roots of the equation
x
2
−
2
x
+
2
=
0
, then least value of
n
for which
(
α
β
)
n
=
1
is:
A
5
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B
4
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C
3
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D
2
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Solution
The correct option is
B
4
(
x
−
1
)
2
+
1
=
0
⇒
x
=
1
±
i
∴
α
β
=
(
1
±
i
1
∓
i
)
=
±
(
2
i
2
)
=
±
i
A
.
T
.
Q
(
α
β
)
n
=
(
±
i
)
n
=
1
⇒
n
=
4
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19
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