Show that it Z1 Z2 Z3
=0 then at least one of the three factors
is zero
Answers
Answer:
a+b+c=0 (1)
and az
1
+bz
2
+z
3
=0 (2)
Since a, b, c are not all zero, from (2), we have
az
1
+bz
2
−(a+b)z
3
=0 [From (1), c=−(a+b)]
or az
1
+bz
2
=(a+b)z
3
or z
3
=
a+b
az
1
+bz
2
(3)
From (3), it follows that z
3
divides the line segment joing z
1
and z
3
internally in the ratio b:a
If a and b are of the same sign, then division is in fact internal, and if a and b are of opposite sign, then division is external in the ratio ∣b∣:∣a∣.
Therefore, z
1
,z
2
and z
3
are collinear.
Step-by-step explanation:
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Answer:
z*1=0 z*2=0z*3=0
Step-by-step explanation:
0*0*0*=0