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Byju's Answer
Standard XII
Mathematics
Geometrical Representation of a Complex Number
Find the locu...
Question
Find the locus of a complex number
z
=
x
+
i
y
satisfying the relation
|
z
+
i
|
=
|
z
+
2
|
. Illustrate the locus of z in the Argand plane.
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Solution
|
z
+
i
|
=
|
z
+
2
|
assume
z
=
x
+
i
y
x
2
+
(
y
+
1
)
2
=
(
x
+
2
)
2
+
y
2
x
2
+
y
2
+
2
y
+
1
=
x
2
+
2
x
+
y
+
y
2
2
y
+
1
=
2
x
+
1
x
=
y
So,
z
=
z
+
i
x
=
x
(
1
+
i
)
So
z
is always multiple pf
(
1
+
i
)
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Similar questions
Q.
Find the locus of a complex number,
z
=
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, satisfying the relation
∣
∣
∣
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i
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∣
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Illustrate the locus of
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Standard XII Mathematics
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