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AMC 12/AHSME
1970 AMC 12/AHSME
5
Evaluating function with imaginary value
Evaluating function with imaginary value
Source: 1970 AHSME Problem 5
March 20, 2014
function
AMC
Problem Statement
If
f
(
x
)
=
x
4
+
x
2
x
+
1
f(x)=\dfrac{x^4+x^2}{x+1}
f
(
x
)
=
x
+
1
x
4
+
x
2
, then
f
(
i
)
f(i)
f
(
i
)
, where
i
=
−
1
i=\sqrt{-1}
i
=
−
1
, is equal to:
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
1
+
i
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
−
1
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
0
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
−
1
−
i
<span class='latex-bold'>(A) </span>1+i\qquad<span class='latex-bold'>(B) </span>1\qquad<span class='latex-bold'>(C) </span>-1\qquad<span class='latex-bold'>(D) </span>0\qquad <span class='latex-bold'>(E) </span>-1-i
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
1
+
i
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
−
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
−
1
−
i
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