Complex multiplication is associative : Order of multiplication can be changed.

*click on the content to continue..*

What does 'Associate' mean?

- to connect with; to join
- to connect with; to join
- to separate

The answer is 'to connect with; to join'

When three complex numbers are multiplies,

• Person A associates the middle complex number with first complex number and, to the result of that, he multiplies the third complex number `(z_1 xx z_2) xx z_3`

• Person B associates the middle complex number with third complex number and to that she multiplies the first complex number `z_1 xx (z_2 xx z_3)` will the two persons get different results?

- They will get different results.
- They will get identical results
- They will get identical results

The answer is 'They will get identical results'.

• Order of multiplication can be changed - associative

**Associative property of Complex Multiplication: **For Any complex number `z_1,z_2,z_3 in CC`,

`z_1 xx (z_2 xx z_3) = (z_1 xx z_2) xx z_3`

Is Associative property applicable to division?

- when Division is handled as inverse of multiplication.
- when Division is handled as inverse of multiplication.
- Order of division can be swapped

The answer is 'when Division is handled as inverse of multiplication'. For `(z_1 -: z_2) -: z_3`, it will be handled `(z_1 xx 1/z_2)xx 1/z_3`, then associative property of multiplication applies.

*Solved Exercise Problem: *

Given `z_1, z_2 in CC`, what will be the result of `z_1 xx (z_2 xx z_1)`?

- `z_1^2 xx z_2`
- `z_1^2 xx z_2`
- `z_1 xx z_2`
- `z_2`

The answer is '`z_1^2 xx z_2`'.

*slide-show version coming soon*