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Question
Mathematics
If z = (√3/2)+(i/2)(i=√-1), then (1+iz+z5+iz8)9 is equal to
Q. If
z
=
2
3
+
2
i
(
i
=
−
1
)
,
then
(
1
+
i
z
+
z
5
+
i
z
8
)
9
is equal to
3129
173
JEE Main
JEE Main 2019
Complex Numbers and Quadratic Equations
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A
−
1
29%
B
1
43%
C
0
7%
D
(
−
1
+
2
i
)
9
21%
Solution:
z
=
2
3
+
2
i
=
cos
6
π
+
i
s
in
6
π
⇒
z
5
=
cos
6
5
π
+
i
s
in
6
5
π
=
2
−
3
+
i
and
Z
8
=
cos
3
4
π
+
i
s
in
3
4
π
=
−
(
2
1
+
i
3
)
⇒
(
1
+
i
z
+
z
5
+
i
z
8
)
9
=
(
1
+
2
i
3
−
2
1
−
2
3
+
2
i
+
2
i
+
2
3
)
9
=
(
2
1
+
i
3
)
9
=
cos
3
π
+
i
s
in
3
π
=
−
1