As the associative law holds, expressions such as a(bc) are equal to (ab)c.Hence there is no need to use brackets.

We know

or

(as i.i=-1)

or

...(1)

or

...(2)(pre-multiplying b/s by j)

Now,

or

(post-multiplying b/s by k)

or

or

...(3)

From(2)&(3)

...(4)

or

(substituting i=jk in 4)

or

(using 2)

or

or

...(5)

or

or

or

...(6)

We have

(equation 5)

or

(substituting j=-ik using 6)

or

or

or

...(7)