Find the number of solutions of the equation .
Solution.
Given that . Hence,
.
.Hence, we get
(since
)
If , we get
.
Thus,
Thus, , that is,
for
. Therefore, the given equation has five solutions.
Find the number of solutions of the equation .
Solution.
Given that . Hence,
.
.Hence, we get
(since
)
If , we get
.
Thus,
Thus, , that is,
for
. Therefore, the given equation has five solutions.
Question: Prove that for any complex number z:
or
Solution: Suppose by way of contradiction that
and
Setting with
yields
.
We obtain
and
and consequently,
and
.
Summing these inequalities implies which is a contradiction.
More later,
Nalin Pithwa