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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.
−
84
\sqrt{-84}
−
84
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.
−
84
\sqrt{-84}
−
84
Use Imaginary Unit:
Now, we know that
−
1
\sqrt{-1}
−
1
is the imaginary unit
i
i
i
. So,
−
84
\sqrt{-84}
−
84
becomes
i
×
84
i \times \sqrt{84}
i
×
84
.
Factor and Simplify:
Next, we simplify
84
\sqrt{84}
84
. The number
84
84
84
can be factored into
4
×
21
4 \times 21
4
×
21
, and
4
4
4
is a perfect square.
\newline
84
=
4
×
21
=
4
×
21
=
2
×
21
\sqrt{84} = \sqrt{4 \times 21} = \sqrt{4} \times \sqrt{21} = 2 \times \sqrt{21}
84
=
4
×
21
=
4
×
21
=
2
×
21
Combine Imaginary Unit:
Now we can combine the imaginary unit with the simplified radical.
i
⋅
84
=
i
⋅
2
⋅
21
i \cdot \sqrt{84} = i \cdot 2 \cdot \sqrt{21}
i
⋅
84
=
i
⋅
2
⋅
21
Multiply to Get Complex Number:
Finally, we multiply the
i
i
i
by
2
2
2
to get the complex number.
i
×
2
×
21
=
2
i
×
21
i \times 2 \times \sqrt{21} = 2i \times \sqrt{21}
i
×
2
×
21
=
2
i
×
21
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Question
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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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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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