level 7
Let
be the magnitude of
. Then the magnitude of
is
, while the magnitude of
is
. We get that
, hence either
or
.
be the magnitude of
. Then the magnitude of
is
, while the magnitude of
is
. We get that
, hence either
or
.
. Multiply both sides by
. The left hand side becomes
, the right hand side becomes
. Hence the solutions for this case are precisely all the
rd complex roots of unity, and there are
of those.