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Byju's Answer
Standard XII
Mathematics
Geometrical Representation of a Complex Number
If sinθ= z -1...
Question
If
sin
θ
=
(
z
−
1
i
)
,
where
z
is non real,
θ
represents angle of a triangle, then
A
R
e
(
z
)
=
1
,
I
m
(
z
)
=
2
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B
R
e
(
z
)
=
1
,
−
1
≤
I
m
(
z
)
≤
1
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C
R
e
(
z
)
+
I
m
(
z
)
=
0
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D
R
e
(
z
)
=
0
,
I
m
(
z
)
=
1
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Solution
The correct option is
B
R
e
(
z
)
=
1
,
−
1
≤
I
m
(
z
)
≤
1
If
θ
represents angle of a triangle, then
sin
θ
must be real.
⇒
z
−
1
i
will be real
Let
z
=
x
+
i
y
,
then
z
−
1
i
=
(
x
+
i
y
)
−
1
i
=
(
x
−
1
)
+
i
y
i
=
(
x
−
1
)
i
i
×
i
+
y
=
y
−
i
(
x
−
1
)
For
y
−
i
(
x
−
1
)
to be real,
x
must be equal to
1
then
sin
θ
=
y
exists if
−
1
≤
y
≤
1
∴
R
e
(
z
)
=
1
and
−
1
≤
I
m
(
z
)
≤
1
Suggest Corrections
0
Similar questions
Q.
s
i
n
−
1
z
−
1
i
where z is non-real, can be the angle of triangle if
Q.
If
z
=
3
2
+
i
2
5
+
3
2
-
i
2
5
,
then
(a) Re (z) = 0
(b) Im (z) = 0
(c) Re (z) > 0, Im (z) > 0
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Q.
If
z
is a complex number satisfying
¯
¯¯¯
¯
z
2
=
1
, where
¯
¯
¯
z
is the conjugate of
z
, then
Q.
If
z
is a complex number satisfying
z
+
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¯
¯
z
=
0
, then
Q.
If
∣
z
−
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R
e
(
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∣
=
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−
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m
(
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∣
,
then z lies on
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