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Byju's Answer
Standard XII
Mathematics
Monotonicity in an Interval
Find the real...
Question
Find the real values of θ for which the complex number
1
+
i
cosθ
1
-
2
i
cosθ
is purely real.
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Solution
1
+
i
cos
θ
1
-
2
i
cos
θ
=
1
+
i
cos
θ
1
-
2
i
cos
θ
×
1
+
2
i
cos
θ
1
+
2
i
cos
θ
=
1
+
2
i
cos
θ
+
i
cos
θ
-
2
cos
θ
1
+
4
cos
2
θ
=
1
-
2
cos
θ
+
i
3
cos
θ
1
+
4
cos
2
θ
For
it
to
be
purely
real
,
the
imaginary
part
must
be
zero
.
3
cos
θ
=
0
This
is
true
for
odd
multiples
of
π
2
.
∴
θ
=
2
n
+
1
π
2
,
n
∈
Z
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Similar questions
Q.
Find the real values of
′
θ
′
for which the complex number
1
+
i
cos
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1
−
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is purely real.
Q.
The real value of θ for which the expression
1
+
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is a real number, is
(a)
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The real value of
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2
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cos
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is real number is
Q.
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