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Byju's Answer
Standard VII
Mathematics
(a-b)^2 Expansion and Visualisation
Find how many...
Question
Find how many nonzero complex numbers
z
satisfy
z
=
i
z
2
.
Open in App
Solution
z
=
i
z
2
Let
z
=
x
+
i
y
z
2
=
(
x
+
i
y
)
2
=
x
2
−
y
2
+
2
i
x
y
i
z
2
=
i
(
x
2
−
y
2
)
−
2
x
y
x
+
2
x
y
=
0
x
(
1
+
2
y
)
=
0
⟹
x
=
0
,
y
=
−
1
2
or,
x
2
−
y
2
=
y
When
x
=
0
y
(
y
+
1
)
=
0
y
=
0
,
y
=
−
1
When
y
=
−
1
2
x
2
−
1
4
=
−
1
2
x
2
=
−
1
4
(not possible)
So, answer is
2
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