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Byju's Answer
Standard XII
Mathematics
Properties of Argument
If Z is a com...
Question
If
z
is a complex number lying in first or fourth quadrant of argand plane satisfying
|
z
−
1
|
=
1.
If
arg
(
z
−
1
)
=
k
arg
(
z
)
,
then the value of
k
is
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Solution
From polar form,
z
−
1
=
cos
θ
+
i
sin
θ
(
∵
|
z
−
1
|
=
1
)
⇒
z
=
1
+
cos
θ
+
i
sin
θ
=
2
cos
2
θ
2
+
2
i
sin
θ
2
cos
θ
2
=
2
cos
θ
2
(
cos
θ
2
+
i
sin
θ
2
)
∴
arg
(
z
)
=
θ
2
=
1
2
arg
(
z
−
1
)
Hence,
arg
(
z
−
1
)
=
2
arg
(
z
)
∴
k
=
2
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|
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Standard XII Mathematics
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