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Let’s check out your problem:
Use the imaginary number
i
i
i
to rewrite the expression below as a complex number. Simplify all radicals.
−
68
\sqrt{-68}
−
68
View step-by-step help
Home
Math Problems
Algebra 2
Introduction to complex numbers
Full solution
Q.
Use the imaginary number
i
i
i
to rewrite the expression below as a complex number. Simplify all radicals.
−
68
\sqrt{-68}
−
68
Split into
Factors
:
Express
−
68
\sqrt{-68}
−
68
as the product of square roots and
−
1
\sqrt{-1}
−
1
.
\newline
−
68
=
−
1
×
68
\sqrt{-68} = \sqrt{-1 \times 68}
−
68
=
−
1
×
68
Express as Complex Number:
Express
−
1
×
68
\sqrt{-1 \times 68}
−
1
×
68
as a complex number using
i
i
i
.
\newline
−
68
=
−
1
×
68
\sqrt{-68} = \sqrt{-1} \times \sqrt{68}
−
68
=
−
1
×
68
Find Prime Factors:
Simplify
68
\sqrt{68}
68
by finding the prime factors of
68
68
68
.
68
=
2
×
2
×
17
68 = 2 \times 2 \times 17
68
=
2
×
2
×
17
Express as
Square Root
:
Express
68
\sqrt{68}
68
as
2
×
2
×
17
\sqrt{2 \times 2 \times 17}
2
×
2
×
17
.
\newline
68
=
4
×
17
\sqrt{68} = \sqrt{4 \times 17}
68
=
4
×
17
Simplify Square Root:
Simplify
4
×
17
\sqrt{4 \times 17}
4
×
17
to
2
×
17
2 \times \sqrt{17}
2
×
17
.
\newline
68
=
2
×
17
\sqrt{68} = 2 \times \sqrt{17}
68
=
2
×
17
Combine Results:
Combine the results to express the original expression as a complex number.
−
68
=
−
1
×
2
×
17
=
2
i
×
17
\sqrt{-68} = \sqrt{-1} \times 2 \times \sqrt{17} = 2i \times \sqrt{17}
−
68
=
−
1
×
2
×
17
=
2
i
×
17
Final Simplification:
Simplify the expression to its final form.
−
68
=
2
i
⋅
17
=
2
i
⋅
17
\sqrt{-68} = 2i \cdot \sqrt{17} = 2i \cdot \sqrt{17}
−
68
=
2
i
⋅
17
=
2
i
⋅
17
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Question
Simplify.
\newline
8
i
+
6
i
8i + 6i
8
i
+
6
i
\newline
\newline
Write your answer in the form
a
+
b
i
a + bi
a
+
bi
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\newline
4
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i
4 + 10i
4
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\newline
\newline
Write your answer in the form
a
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i
a + bi
a
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Simplify.
\newline
−
4
i
−
9
i
\frac{{-4i}}{{-9i}}
−
9
i
−
4
i
\newline
\newline
Write your simplified answer in the form
a
+
b
i
a + bi
a
+
bi
.
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Question
Combine the like terms to create an equivalent expression.
\newline
7
k
−
k
+
19
=
0
7k-k+19=\boxed{\phantom{0}}
7
k
−
k
+
19
=
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Apply the distributive property to factor out the greatest common factor.
\newline
9
+
12
n
=
9+12 n=
9
+
12
n
=
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Question
Solve the equation.
\newline
12
=
n
−
9
n
=
□
\begin{aligned} & 12=n-9 \\ n= & \square \end{aligned}
n
=
12
=
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−
9
□
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Posted 1 year ago
Question
What is the amplitude of
y
=
−
sin
(
8
x
−
3
)
+
5
y=-\sin (8 x-3)+5
y
=
−
sin
(
8
x
−
3
)
+
5
?
\newline
units
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Posted 1 year ago
Question
What is the period of
\newline
y
=
4
sin
(
−
2
x
+
7
)
−
1
?
y=4 \sin (-2 x+7)-1 \text { ? }
y
=
4
sin
(
−
2
x
+
7
)
−
1
?
\newline
Give an exact value.
\newline
units
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Posted 1 year ago
Question
3
⋅
(
3
+
20
i
)
=
3 \cdot(3+20 i)=
3
⋅
(
3
+
20
i
)
=
\newline
Your answer should be a complex number in the form
a
+
b
i
a+b i
a
+
bi
where
a
a
a
and
b
b
b
are real numbers.
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Posted 1 year ago
Question
(
35
−
23
i
)
+
(
13
+
25
i
)
=
(35-23 i)+(13+25 i)=
(
35
−
23
i
)
+
(
13
+
25
i
)
=
\newline
Express your answer in the form
(
a
+
b
i
)
(a+b i)
(
a
+
bi
)
.
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Posted 1 year ago
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