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TS EAMCET 20-July-2022 Shift 1 Solved Paper
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© examsnet.com
Question : 8
Total: 160
If
|
x
+
i
y
|
=
√
x
2
+
y
2
, then
|
(
1
−
√
3
i
)
9
+
(
√
3
+
i
)
9
|
=
2
9
2
18
2
10
2
19
2
Validate
Solution:
👈: Video Solution
Given,
|
x
+
i
y
|
=
√
x
2
+
y
2
Since,
(
1
−
√
3
i
)
9
+
(
√
3
+
i
)
9
=
i
−
9
(
1
i
−
√
3
)
9
+
(
√
3
+
i
)
9
[
∵
i
−
9
=
1
i
9
=
1
i
8
⋅
i
=
1
(
i
2
)
4
i
=
1
(
−
1
)
4
i
=
1
i
=
−
i
]
Now,
|
(
1
−
√
3
i
)
9
+
(
√
3
+
i
)
9
|
=
|
(
i
+
√
3
)
9
(
i
+
1
)
|
=
|
i
+
1
|
|
(
i
+
√
3
)
9
|
=
|
i
+
1
|
|
i
+
√
3
|
9
=
(
√
1
2
+
1
2
)
(
√
1
2
+
(
√
3
)
2
)
9
=
√
2
(
√
4
)
9
=
2
1
2
⋅
2
9
=
2
19
2
© examsnet.com
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