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Standard VIII
Mathematics
Locating a Given Point on a Graph Paper
16. The compl...
Question
16. The complex numbers z1,z2,z3 are the vertices of a triangle . Then the complex number z which make the triangle into parallelogram is A)z1+z2-z3. B)z1-z2+z3 C)z2+z3-z1. D) all of these
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Q.
If the complex numbers,
z
1
,
z
2
,
z
3
represent the vertices of an equilateral triangle such that
|
z
1
|
=
|
z
2
|
=
|
z
3
|
,
then
z
1
+
z
2
+
z
3
=
Q.
If the complex numbers
z
1
,
z
2
,
z
3
represent the the vertices of an equilateral triangle such that
|
z
1
|
=
|
z
2
|
=
|
z
3
|
, then prove that
z
1
+
z
2
+
z
3
=
0
Q.
The complex numbers
z
1
,
z
2
and
z
3
satisfying
z
1
−
z
3
z
2
−
z
3
=
1
−
√
3
i
2
are the vertices of a triangle which is:
Q.
The complex numbers
z
1
,
z
2
,
z
3
are the vertices of a triangle. Find all the complex numbers
z
which make the triangle into a parallelogram.
Q.
Assertion :Let
z
1
,
z
2
,
z
3
be distinct complex numbers &
ω
3
=
1
,
ω
≠
1
If
z
+
ω
z
2
+
ω
2
z
3
=
0
then
z
1
,
z
2
,
z
3
are the vertices of an equilateral triangle. Reason: If
z
3
−
z
1
=
(
z
2
−
z
1
)
e
−
1
π
/
3
then
z
1
,
z
2
,
z
3
are vertices of an equilateral triangle.
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