Talk:2.10.6/@comment-140.180.190.171-20120620030417/@comment-5149782-20120620102713

The coset thing is hopefully fixed now, the previous (incorrect) answer was:

"Let $a$, $b$ be non-negative real numbers, and note that $(a+bi)H = (a-bi)H = (-a+bi)H = (-a-bi)H.$ When either $a$ or $b$ (but not both) equals $0$ we furthermore see that $aH = -aH = (bi)H = (-bi)H.$"