Tardigrade
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Tardigrade
Question
Mathematics
If ω = ( (z-i /1+iz) )n n integral, then ω lies on the unit circle for the unit circle for
Q. If
ω
=
(
1
+
i
z
z
−
i
)
n
n
integral, then
ω
lies on the unit circle for the unit circle for
1441
203
Complex Numbers and Quadratic Equations
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A
only even
n
12%
B
only odd
n
38%
C
only positive
n
38%
D
all
n
12%
Solution:
ω
=
(
1
+
i
z
z
−
1
)
n
=
[
i
(
z
−
i
)
z
−
i
]
n
=
(
i
1
)
n
=
(
−
i
)
n
∴
∣
ω
∣
=
∣
(
−
i
)
n
∣
=
∣
−
i
∣
n
=
1
for all
n
.
∴
ω
lies on unit circle for of all
n
.