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Standard XII
Mathematics
Modulus of a Complex Number
Question
State true or false:
The complex numbers
z
=
x
+
i
y
which satisfy the equation
∣
∣
∣
z
−
5
i
z
+
5
i
∣
∣
∣
=
1
lie on the axis of
Y
.
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Solution
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∣
∣
∣
z
−
5
i
z
+
5
i
∣
∣
∣
=
1
or

x
+
i
y
−
5
i

2
=

x
+
i
y
+
5
i

2
or
x
2
+
(
y
−
5
)
2
=
x
2
+
(
y
+
5
)
2
or
20
y
=
0
or
y
=
0
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Similar Questions
Q1
State true or false:
The complex numbers
z
=
x
+
i
y
which satisfy the equation
∣
∣
∣
z
−
5
i
z
+
5
i
∣
∣
∣
=
1
lie on the axis of
Y
.
View Solution
Q2
Prove that complex number
z
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x
+
i
y
which satisfy the equation
∣
∣
∣
z
−
5
i
z
+
5
i
∣
∣
∣
=
1
lie on the axis of
x
.
View Solution
Q3
The complex numbers
z
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i
y
which satisfy equation
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5
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5
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∣
∣
∣
=
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lie on
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Q4
The complex numbers
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∣
∣
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i
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∣
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Q5
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