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Byju's Answer
Standard XII
Mathematics
Conjugate of a Complex Number
Find all non-...
Question
Find all non-zero complex number
Z
satisfying
¯
¯¯
¯
Z
=
i
Z
2
.
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Solution
Let,
Z
=
x
+
i
y
.
Given,
¯
¯¯
¯
Z
=
i
Z
2
or,
x
−
i
y
=
i
(
x
2
−
y
2
+
2
i
x
y
)
Comparing the real and imaginary part both sides we get,
x
=
−
2
y
x
and
−
y
=
x
2
−
y
2
.......(1).
or,
y
=
−
1
2
[ Since
Z
is non-zero].
Using the value of
y
in (1) we get,
x
2
=
3
4
or,
x
=
±
√
3
2
So
Z
=
(
±
√
3
2
,
−
1
2
)
.
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