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Let’s check out your problem:
Express the radical using the imaginary unit,
i
i
i
.
\newline
Express your answer in simplified form.
\newline
±
−
4
=
±
\pm \sqrt{-4}= \pm
±
−
4
=
±
View step-by-step help
Home
Math Problems
Algebra 2
Introduction to complex numbers
Full solution
Q.
Express the radical using the imaginary unit,
i
i
i
.
\newline
Express your answer in simplified form.
\newline
±
−
4
=
±
\pm \sqrt{-4}= \pm
±
−
4
=
±
Express as product of square roots:
Express
±
−
4
\pm\sqrt{-4}
±
−
4
as the product of square roots and
−
1
\sqrt{-1}
−
1
.
\newline
±
−
4
=
±
−
1
⋅
4
\pm\sqrt{-4} = \pm\sqrt{-1 \cdot 4}
±
−
4
=
±
−
1
⋅
4
Recognize imaginary unit:
Recognize that
−
1
\sqrt{-1}
−
1
is the imaginary unit
i
i
i
.
\newline
±
−
4
=
±
−
1
⋅
4
\pm\sqrt{-4} = \pm\sqrt{-1} \cdot \sqrt{4}
±
−
4
=
±
−
1
⋅
4
Simplify square root of
4
4
4
:
Simplify the
square root
of
4
4
4
, which is
2
2
2
.
\newline
±
−
4
=
±
i
×
2
\pm\sqrt{-4} = \pm i \times 2
±
−
4
=
±
i
×
2
Combine
±
\pm
±
and
2
2
2
for final form:
Combine the
±
\pm
±
and the
2
2
2
to get the final simplified form.
\newline
±
−
4
=
±
2
i
\pm\sqrt{-4} = \pm 2i
±
−
4
=
±
2
i
More problems from Introduction to complex numbers
Question
What is the period of
y
=
3
cos
(
x
−
7
)
+
2
y=3 \cos (x-7)+2
y
=
3
cos
(
x
−
7
)
+
2
?
\newline
Give an exact value.
\newline
units
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Posted 10 months ago
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(
−
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(
−
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i
)
+
(
−
40
+
8
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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Posted 10 months ago
Question
(
8
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−
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−
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)
=
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−
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)
−
(
−
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+
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)
=
\newline
Express your answer in the form
(
a
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b
i
)
(a+b i)
(
a
+
bi
)
.
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Posted 10 months ago
Question
(
80
i
)
−
(
80
+
10
i
)
=
(80 i)-(80+10 i)=
(
80
i
)
−
(
80
+
10
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
Get tutor help
Posted 10 months ago
Question
Express the radical using the imaginary unit,
i
i
i
.
\newline
Express your answer in simplified form.
\newline
±
−
64
=
±
\pm \sqrt{-64}= \pm
±
−
64
=
±
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Posted 10 months ago
Question
Which of the following is equivalent to the complex number
i
21
i^{21}
i
21
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
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Posted 10 months ago
Question
Express the radical using the imaginary unit,
i
i
i
.
\newline
Express your answer in simplified form.
\newline
±
−
30
=
±
\pm \sqrt{-30}= \pm
±
−
30
=
±
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Posted 10 months ago
Question
Express the radical using the imaginary unit,
i
i
i
.
\newline
Express your answer in simplified form.
\newline
±
−
35
=
±
\pm \sqrt{-35}= \pm
±
−
35
=
±
Get tutor help
Posted 10 months ago
Question
Express the radical using the imaginary unit,
i
i
i
.
\newline
Express your answer in simplified form.
\newline
±
−
80
=
±
\pm \sqrt{-80}= \pm
±
−
80
=
±
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Posted 10 months ago
Question
You pick a card at random, put it back, and then pick another card at random.
\newline
4
4
4
\newline
5
5
5
\newline
6
6
6
\newline
7
7
7
\newline
What is the probability of picking a number greater than
5
5
5
and then picking a
4
4
4
?
\newline
Write your answer as a percentage.
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Posted 1 month ago
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