Question

show that the only quaternions commutimg with i are of the form a+ bi

Answer 1

Any ideas?

Answer 2

A general quaternion is of the form q = a + bi + cj + dk. We have
qi = −b + ai + dj − ck and iq = −b + ai − dj + ck.
For these to be equal, we must have
d = −d and c = −c.
As c and d are real numbers, it follows that c = d = 0.
Thus the only quaternions that commute with i are of the form a + bi.

Answer 3

is it right?

Answer 4

Yeah that look perfect to me.

Answer 5

ok thanks