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Byju's Answer
Standard XIII
Mathematics
Distance Formula Using Complex Numbers
If z = x + iy...
Question
If
z
=
x
+
i
y
,
z
1
/
3
=
a
−
i
b
and
x
a
−
y
b
=
k
(
a
2
−
b
2
)
,
then
k
=
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Solution
(
x
+
i
y
)
1
/
3
=
a
−
i
b
⇒
x
+
i
y
=
(
a
−
i
b
)
3
⇒
x
+
i
y
=
(
a
3
−
3
a
b
2
)
+
i
(
b
3
−
3
a
2
b
)
⇒
x
=
a
3
−
3
a
b
2
,
y
=
b
3
−
3
a
2
b
∴
x
a
−
y
b
=
a
2
−
3
b
2
−
b
2
+
3
a
2
=
4
(
a
2
−
b
2
)
Hence
k
=
4
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Distance Formula Using Complex Numbers
Standard XIII Mathematics
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