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Byju's Answer
Standard XII
Mathematics
Scalar Triple Product
if z1= 7-3i,...
Question
if z
1
= 7-3i, z
2
= 3 + root3 i , z
3
=4-8i, then find z
1
z
2
z
3
.
Open in App
Solution
z
1
=
7
-
3
i
z
2
=
3
+
3
i
z
3
=
4
-
8
i
S
o
,
z
1
z
2
z
3
=
(
7
-
3
i
)
(
3
+
3
i
)
(
4
-
8
i
)
=
(
21
+
7
3
i
-
9
i
-
3
3
i
2
)
(
4
-
8
i
)
=
(
21
+
7
3
i
-
9
i
-
3
3
(
-
1
)
)
(
4
-
8
i
)
A
s
i
2
=
-
1
=
(
21
+
7
3
i
-
9
i
+
3
3
)
(
4
-
8
i
)
=
84
-
168
i
+
28
3
i
-
56
3
i
2
-
36
i
+
72
i
2
+
12
3
-
24
3
i
=
84
-
168
i
+
28
3
i
-
56
3
(
-
1
)
-
36
i
+
72
(
-
1
)
+
12
3
-
24
3
i
=
84
-
168
i
+
28
3
i
+
56
3
-
36
i
-
72
+
12
3
-
24
3
i
=
12
-
204
i
+
4
3
i
+
68
3
=
12
+
68
3
-
i
(
51
-
3
)
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0
Similar questions
Q.
If
z
1
=
1
+
2
i
,
z
2
=
2
+
3
i
,
z
3
=
3
+
4
i
, then
z
1
,
z
2
and
z
3
are collinear.
Q.
let
z
1
=
1
+
i
and
z
2
=
−
1
−
i
. Find
z
3
∈
C
such that triangle
z
1
z
2
z
3
is equilateral.
Q.
If
z
1
=
1
+
2
i
,
z
2
=
2
+
3
i
,
z
3
=
3
+
4
i
,
then
z
1
,
z
2
and
z
3
represent the vertices of
Q.
If
z
1
,
z
2
,
z
3
are
3
distinct complex numbers such that
3
|
z
2
−
z
3
|
=
4
|
z
3
−
z
1
|
=
5
|
z
1
−
z
2
|
, then the value of
9
z
2
−
z
3
+
16
z
3
−
z
1
+
25
z
1
−
z
2
equals
Q.
Assertion :Number of solutions of complex number
z
satisfying
|
z
−
1
−
2
i
|
=
|
z
−
2
−
3
i
|
=
|
z
−
3
|
is one Reason: If
z
1
≠
z
2
≠
z
3
, then
|
z
−
z
1
|
=
|
z
−
z
2
|
=
|
z
−
z
3
|
has one solution.
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