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Byju's Answer
Standard XIII
Mathematics
Purely Real
If w=-9+3i1-2...
Question
If
w
=
−
9
+
3
i
1
−
2
i
, then
A
|
w
|
=
3
√
2
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B
arg
w
=
π
4
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C
|
w
|
=
√
2
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D
arg
w
=
−
3
π
4
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Solution
The correct option is
D
arg
w
=
−
3
π
4
w
=
−
9
+
3
i
1
−
2
i
⇒
w
=
(
−
9
+
3
i
)
(
1
+
2
i
)
(
1
−
2
i
)
(
1
+
2
i
)
⇒
w
=
−
9
−
18
i
+
3
i
−
6
1
+
4
⇒
w
=
−
15
−
15
i
5
=
−
3
−
3
i
|
w
|
=
|
−
3
−
3
i
|
=
√
(
−
3
)
2
+
(
−
3
)
2
∴
|
w
|
=
3
√
2
Now,
tan
α
=
(
∣
∣
∣
−
3
−
3
∣
∣
∣
)
=
1
⇒
α
=
π
4
As
w
lies in third quadrant, so
arg
w
=
−
(
π
−
α
)
=
−
(
π
−
π
4
)
∴
arg
w
=
−
3
π
4
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0
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