Using Conjugates with Complex Numbers
Algebra 2 · Flashcards
ALGEBRA 2 · FLASHCARDS
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QUESTION
State the formula for the modulus of
z
=
a
+
b
i
z=a+bi
z
=
a
+
bi
.
QUESTION
What is
∣
3
+
4
i
1
−
2
i
∣
\left|\frac{3+4i}{1-2i}\right|
1
−
2
i
3
+
4
i
?
QUESTION
What is
4
1
−
3
i
\frac{4}{1-3i}
1
−
3
i
4
written as
a
+
b
i
a+bi
a
+
bi
?
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ANSWER
2
5
+
6
5
i
\frac{2}{5}+\frac{6}{5}i
5
2
+
5
6
i
. Multiply by conjugate
1
+
3
i
1+3i
1
+
3
i
:
4
(
1
+
3
i
)
(
1
−
3
i
)
(
1
+
3
i
)
=
4
+
12
i
10
\frac{4(1+3i)}{(1-3i)(1+3i)}=\frac{4+12i}{10}
(
1
−
3
i
)
(
1
+
3
i
)
4
(
1
+
3
i
)
=
10
4
+
12
i
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