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Math Problems
Precalculus
Convert complex numbers between rectangular and polar form
30
30
30
. An irrational number between
5
5
5
and
6
6
6
is
\newline
(a)
1
2
(
5
+
6
)
\frac{1}{2}(5+6)
2
1
(
5
+
6
)
\newline
(b)
5
+
6
\sqrt{5+6}
5
+
6
\newline
(c)
5
×
6
\sqrt{5 \times 6}
5
×
6
\newline
(d) none of these
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Which of the following is equal to
sin
(
π
5
)
\sin \left( \frac{\pi}{5} \right)
sin
(
5
π
)
?
\newline
A)
−
cos
(
π
5
)
-\cos \left( \frac{\pi}{5} \right)
−
cos
(
5
π
)
\newline
B)
−
sin
(
π
5
)
-\sin \left( \frac{\pi}{5} \right)
−
sin
(
5
π
)
\newline
C)
cos
(
3
π
10
)
\cos \left( \frac{3\pi}{10} \right)
cos
(
10
3
π
)
\newline
D)
sin
(
7
π
10
)
\sin\left( \frac{7\pi}{10} \right)
sin
(
10
7
π
)
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8
8
8
:
52
52
52
PM
∣
155
K
B
/
s
\mid 155 \mathrm{~KB} / \mathrm{s}
∣
155
KB
/
s
\newline
Edit
\newline
Assignment
3
3
3
\newline
1
1
1
. Consider the complex number (MARCH
−
2012
-2012
−
2012
)
\newline
z
=
5
−
3
i
4
+
2
3
i
z=\frac{5-\sqrt{3} i}{4+2 \sqrt{3} i}
z
=
4
+
2
3
i
5
−
3
i
\newline
i) Express complex number in the form of
a
+
i
b
a+i b
a
+
ib
.
\newline
ii) Express complex number in the polar form
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Assignment
3
3
3
\newline
Consider the complex number (MARCH
−
2012
-2012
−
2012
)
\newline
z
=
5
−
3
4
4
+
2
3
z=\frac{5-\sqrt{3} 4}{4+2 \sqrt{3}}
z
=
4
+
2
3
5
−
3
4
\newline
i) Express complex number in the form of a + ib.
\newline
ii) Express complex number in the polar form
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Assignment
3
3
3
\newline
1
1
1
. Consider the complex number (MARCH
−
2012
-2012
−
2012
)
\newline
z
=
5
−
3
i
4
+
2
3
i
z=\frac{5-\sqrt{3} i}{4+2 \sqrt{3} i}
z
=
4
+
2
3
i
5
−
3
i
\newline
i) Express complex number in the form of
a
+
\mathrm{a}+
a
+
in
\newline
ii) Express complex number in the polar form
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Write the complex number in polar form with argument
θ
\theta
θ
between
0
0
0
and
2
π
2\pi
2
π
.
−
2
+
2
i
-2 + 2i
−
2
+
2
i
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Use symmetry to graph the polar curve and identify the type of curve.
\newline
r
=
3
+
3
cos
θ
r=3+3 \cos \theta
r
=
3
+
3
cos
θ
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In the expansion of
(
1
−
3
b
)
n
(1-3b)^n
(
1
−
3
b
)
n
in ascending powers of
b
b
b
, the coefficient of the third term is
324
324
324
. Find the value of
n
n
n
using the binomial theorem.
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Use polar coordinates to find the volume of the given solid.
\newline
bounded by the paraboloids
z
=
12
−
x
2
−
y
2
z=12-x^{2}-y^{2}
z
=
12
−
x
2
−
y
2
and
z
=
5
x
2
+
5
y
2
z=5 x^{2}+5 y^{2}
z
=
5
x
2
+
5
y
2
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Use polar coordinates to find the volume of the given solid.
\newline
above the cone
z
=
x
2
+
y
2
z=\sqrt{x^{2}+y^{2}}
z
=
x
2
+
y
2
and below the sphere
x
2
+
y
2
+
z
2
=
81
x^{2}+y^{2}+z^{2}=81
x
2
+
y
2
+
z
2
=
81
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e) A fraction with
2
2
2
mixed radicals in the numerator and
2
2
2
mixed radicals in the denominator whose result contains a perfect square in the numerator when rationalized.
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Express as a complex number in simplest a+bi form:
\newline
14
−
28
i
1
+
3
i
\frac{14-28 i}{1+3 i}
1
+
3
i
14
−
28
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
9
−
2
i
−
7
−
3
i
\frac{9-2 i}{-7-3 i}
−
7
−
3
i
9
−
2
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
4
−
22
i
2
+
4
i
\frac{4-22 i}{2+4 i}
2
+
4
i
4
−
22
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
−
9
−
6
i
−
5
+
2
i
\frac{-9-6 i}{-5+2 i}
−
5
+
2
i
−
9
−
6
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
−
19
−
i
10
−
9
i
\frac{-19-i}{10-9 i}
10
−
9
i
−
19
−
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
22
−
24
i
2
−
7
i
\frac{22-24 i}{2-7 i}
2
−
7
i
22
−
24
i
\newline
Answer:
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Express as a complex number in simplest a+bi form:
\newline
6
−
6
i
2
−
i
\frac{6-6 i}{2-i}
2
−
i
6
−
6
i
\newline
Answer:
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2
2
2
. [
1
1
1
/
1
1
1
Points]
\newline
DETAILS
\newline
MY NOTES
\newline
Find the standard form of the equation of the hyperbola with the given characteristics.
\newline
Vertices:
(
±
6
,
0
)
( \pm 6,0)
(
±
6
,
0
)
; foci:
(
±
9
,
0
)
( \pm 9,0)
(
±
9
,
0
)
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Find the inverse
\newline
f
(
x
)
=
2
x
−
7
3
f(x)=\sqrt[3]{2x-7}
f
(
x
)
=
3
2
x
−
7
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Write
3
[
cos
(
π
2
)
+
i
sin
(
π
2
)
]
3\left[\cos \left(\frac{\pi}{2}\right)+i \sin \left(\frac{\pi}{2}\right)\right]
3
[
cos
(
2
π
)
+
i
sin
(
2
π
)
]
in rectangular form.
\newline
Simplify any radicals.
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Convert the polar equation
\newline
r
=
5
2
sin
θ
−
3
cos
θ
r=\frac{5}{2\sin \theta-3\cos \theta}
r
=
2
s
i
n
θ
−
3
c
o
s
θ
5
to rectangular form.
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Convert the equation to polar form. (Use variables
r
r
r
and
θ
\theta
θ
as needed.)
\newline
y
=
6
x
2
y=6x^{2}
y
=
6
x
2
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