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If
z
=
(
3
2
+
i
2
)
5
+
(
3
2
−
i
2
)
5
z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5
z
=
(
2
3
+
2
i
)
5
+
(
2
3
−
2
i
)
5
…
Mathematics
Problem
If
z
=
(
3
2
+
i
2
)
5
+
(
3
2
−
i
2
)
5
z = \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)^5 + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)^5
z
=
(
2
3
+
2
i
)
5
+
(
2
3
−
2
i
)
5
, then (1)
Re
(
z
)
=
0
\operatorname{Re}(z) = 0
Re
(
z
)
=
0
(2)
Im
(
z
)
=
0
\operatorname{Im}(z) = 0
Im
(
z
)
=
0
(3)
Re
(
z
)
>
0
,
Im
(
z
)
>
0
\operatorname{Re}(z) > 0, \operatorname{Im}(z) > 0
Re
(
z
)
>
0
,
Im
(
z
)
>
0
(4)
Re
(
z
)
>
0
,
Im
(
z
)
<
0
\operatorname{Re}(z) > 0, \operatorname{Im}(z) < 0
Re
(
z
)
>
0
,
Im
(
z
)
<
0
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