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Byju's Answer
Standard XIII
Mathematics
Cube Root of a Complex Number
Let z0 be a r...
Question
Let
z
0
be a root of the quadratic equation,
x
2
+
x
+
1
=
0
. If
z
=
3
+
6
i
z
81
0
−
3
i
z
93
0
, then
arg
z
is equal to :
A
π
4
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B
π
6
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C
π
3
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D
0
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Solution
The correct option is
A
π
4
Roots of
x
2
+
x
+
1
=
0
are
ω
and
ω
2
, where
ω
is the cube root of unity.
Let
z
0
=
ω
Thus,
z
=
3
+
6
i
(
ω
)
81
−
3
i
(
ω
)
93
=
3
+
6
i
−
3
i
[
∵
ω
3
=
1
]
=
3
+
3
i
arg
(
z
)
=
tan
−
1
(
3
3
)
=
tan
−
1
(
1
)
⇒
arg
(
z
)
=
π
4
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Cube Root of a Complex Number
Standard XIII Mathematics
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