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Byju's Answer
Standard XII
Mathematics
Slope Form a Line
Prove that th...
Question
Prove that the roots of
(
z
−
1
)
n
=
i
(
z
+
1
)
n
when plotted in the Argand plane are collinear.
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Solution
we have
(
z
−
1
)
n
=
i
(
z
+
1
)
n
∴
|
z
−
1
|
n
=
|
i
|
|
z
+
1
|
n
or
|
z
−
1
|
n
=
|
z
+
1
|
n
or
|
z
−
1
|
=
|
z
+
1
|
or
|
z
−
1
|
2
=
|
z
+
1
|
2
⟹
(
x
−
1
)
2
+
y
2
=
(
x
+
1
)
2
+
y
2
or
4
x
=
0
or
x
=
0
Therefore, the roots lie on the y-axis.
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