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Problems
If
z
r
=
cos
(
r
α
n
2
)
+
i
sin
(
r
α
n
2
)
z_r = \cos\left(\frac{r\alpha}{n^2}\right) + i \sin\left(\frac{r\alpha}{n^2}\right)
z
r
=
cos
(
n
2
r
α
)
+
i
sin
(
n
2
r
α
)
,…
Mathematics
Problem
If
z
r
=
cos
(
r
α
n
2
)
+
i
sin
(
r
α
n
2
)
z_r = \cos\left(\frac{r\alpha}{n^2}\right) + i \sin\left(\frac{r\alpha}{n^2}\right)
z
r
=
cos
(
n
2
r
α
)
+
i
sin
(
n
2
r
α
)
, where
r
=
1
,
2
,
3
,
…
,
n
r = 1, 2, 3, \dots, n
r
=
1
,
2
,
3
,
…
,
n
and
i
=
−
1
i = \sqrt{-1}
i
=
−
1
, then
lim
n
→
∞
z
1
z
2
z
3
…
z
n
\lim_{n \to \infty} z_1 z_2 z_3 \dots z_n
lim
n
→
∞
z
1
z
2
z
3
…
z
n
is equal to a.
e
i
α
e^{i\alpha}
e
i
α
b.
e
−
i
α
/
2
e^{-i\alpha/2}
e
−
i
α
/2
c.
e
i
α
/
2
e^{i\alpha/2}
e
i
α
/2
d.
e
i
α
3
\sqrt[3]{e^{i\alpha}}
3
e
i
α
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