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KEAM 2016 Math Paper
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© examsnet.com
Question : 7
Total: 120
The principal argument of the complex number
z
=
1
+
s
i
n
π
3
+
i
cos
π
3
1
+
s
i
n
π
3
−
i
cos
π
3
is
π
3
π
6
2
π
3
π
2
π
4
Validate
Solution:
arg (z)=arg (Numerator)-arg (Denominator)
=
tan
−
1
|
cos
π
3
1
+
sin
π
3
|
+
tan
−
1
|
cos
π
3
1
+
sin
π
3
|
=
2
tan
−
1
[
cos
π
3
1
+
sin
π
3
]
=
2
tan
−
1
(
2
−
√
3
)
=
2
×
15
∘
=
30
∘
=
π
6
© examsnet.com
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