Question

How does commutative property of multiplication apply for complex numbers, give an example?

Answer 1

Example for comutative property of multiplication is `(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)`

Explanation:

Commutative Property of multiplication means for two numbers `a` and `b`, `axxb=bxxa` or `ab=ba`

Here what we have are complex numbers and for complex numbers, this means that for two complex numbers `a+bi` and `c+di`, we have

`(a+bi)(c+di)=(c+di)(a+bi)`

Hence example for commutative property of multiplication is

`(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)`

Let us solve both sides separately, using `i^2=-1`,

`(4+2i)(3-5i)=4xx3+4xx(-5i)+(2i)xx3+(2i)xx(-5i)`

= `12-20i+6i-10i^2=12-20i+6i+10=22-14i` and

`(3-5i)(4+2i)=3xx4+3xx2i+(-5i)xx4+(-5i)xx(2i)`

= `12+6i-20i-10i^2=12+6i-20i+10=22-14i`