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Welcome to Bytelearn!
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.
−
−
60
-\sqrt{-60}
−
−
60
View step-by-step help
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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.
−
−
60
-\sqrt{-60}
−
−
60
Express as product:
First, let's express
−
−
60
-\sqrt{-60}
−
−
60
as the product of square roots and
−
1
\sqrt{-1}
−
1
.
\newline
−
−
60
=
−
−
1
×
60
-\sqrt{-60} = -\sqrt{-1 \times 60}
−
−
60
=
−
−
1
×
60
Rewrite and simplify:
Now, let's rewrite
−
−
1
-\sqrt{-1}
−
−
1
as
i
i
i
and
60
\sqrt{60}
60
as
4
×
15
\sqrt{4\times15}
4
×
15
to simplify the radical.
\newline
−
−
60
=
−
i
×
4
×
15
-\sqrt{-60} = -i \times \sqrt{4\times15}
−
−
60
=
−
i
×
4
×
15
Simplify radical:
We know that
4
\sqrt{4}
4
is
2
2
2
, so we can simplify further.
\newline
−
i
⋅
4
⋅
15
=
−
i
⋅
4
⋅
15
-i \cdot \sqrt{4\cdot15} = -i \cdot \sqrt{4} \cdot \sqrt{15}
−
i
⋅
4
⋅
15
=
−
i
⋅
4
⋅
15
Do multiplication:
Now, let's do the multiplication.
\newline
−
i
×
4
×
15
=
−
i
×
2
×
15
-i \times \sqrt{4} \times \sqrt{15} = -i \times 2 \times \sqrt{15}
−
i
×
4
×
15
=
−
i
×
2
×
15
Final complex number:
Finally, we multiply
−
i
-i
−
i
by
2
2
2
to get the simplified complex number.
−
i
×
2
×
15
=
−
2
i
×
15
-i \times 2 \times \sqrt{15} = -2i \times \sqrt{15}
−
i
×
2
×
15
=
−
2
i
×
15
More problems from Introduction to complex numbers
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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Question
Find the complex conjugate of the given number.
\newline
4
+
10
i
4 + 10i
4
+
10
i
\newline
\newline
Write your answer in the form
a
+
b
i
a + bi
a
+
bi
.
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Question
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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Posted 9 months ago
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
=
0
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Posted 1 year ago
Question
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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Posted 9 months ago
Question
Solve the equation.
\newline
12
=
n
−
9
n
=
□
\begin{aligned} & 12=n-9 \\ n= & \square \end{aligned}
n
=
12
=
n
−
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.
Get tutor help
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
)
.
Get tutor help
Posted 1 year ago
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