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13
Math Prize 2023 Problem 13
Math Prize 2023 Problem 13
Source:
October 11, 2023
Problem Statement
Let
f
(
t
)
=
(
10
+
9
i
)
t
−
10
+
9
i
t
+
i
,
f(t) = \frac{(10 + 9i)t - 10 + 9i}{t + i} ,
f
(
t
)
=
t
+
i
(
10
+
9
i
)
t
−
10
+
9
i
,
where
i
=
−
1
i=\sqrt{-1}
i
=
−
1
. Let
P
=
f
(
0
)
P = f(0)
P
=
f
(
0
)
,
Q
=
f
(
2023
)
Q = f(2023)
Q
=
f
(
2023
)
, and
R
=
f
(
1
)
R = f(1)
R
=
f
(
1
)
. Determine
sin
2
(
m
∠
P
Q
R
)
\sin^2(m\angle PQR)
sin
2
(
m
∠
PQR
)
.
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