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Byju's Answer
Standard XI
Mathematics
Equation of Circle in Complex Form
If Re 1z>12 a...
Question
If
R
e
(
1
z
)
>
1
2
and
R
e
(
z
)
>
0
, then which of the following is/are true about the locus of
z
?
A
The locus of
z
is the region inside a circle.
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B
The locus of
z
is the region inside an ellipse.
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C
Area of locus is
π
sq. units
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D
Centre of the locus is
(
1
,
0
)
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Solution
The correct option is
D
Centre of the locus is
(
1
,
0
)
Let
z
=
x
+
i
y
1
z
=
1
x
+
i
y
⇒
1
z
=
x
−
i
y
x
2
+
y
2
As
R
e
(
1
z
)
>
1
2
, so
x
x
2
+
y
2
>
1
2
⇒
2
x
>
x
2
+
y
2
⇒
x
2
+
y
2
−
2
x
<
0
⇒
(
x
−
1
)
2
+
y
2
<
1
It's the interior region of the circle with centre
(
1
,
0
)
and the radius is
1
unit
Area is less than
π
sq. units
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0
Similar questions
Q.
If
R
e
(
1
z
)
>
1
2
and
R
e
(
z
)
>
0
, then which of the following is/are true about the locus of
z
?
Q.
If
R
e
(
1
z
)
>
1
2
and
R
e
(
z
)
>
0
, then which of the following is/are true about the locus of
z
?
Q.
If
R
e
z
2
=
0
then the locus of z is
Q.
If
α
,
β
are the roots of
2
x
2
+
3
x
+
1
=
0
, then the equation whose roots are
1
α
,
1
β
is
Q.
A point
P
is taken on
′
L
′
such that
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P
=
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+
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B
.
Then the locus of
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is :
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