Question

How do you evaluate `(6- i \sqrt { 2} ) ( 6+ i \sqrt { 2} )`?

Answer 1

Expand the expression using the FOIL method.

Explanation:

So all we're doing is expanding the brackets.

We can do this by using the FOIL method.

Now looking at the expression, we see a positive and negative `b` and `d` value. You can think of this as an expanded form of a difference of squares (`a^2-b^2)`.

If we apply this concept to this expression, that means there will be no middle value.

`(6-isqrt2)(6+isqrt2)`

`=36-2i^2`

`=~2i^2 +36`

If we equate this expression to `0`, then...

`0=~2i^2 +36`

`~36=~2i^2`

`18=i^2`

`sqrt18=i`

Hope this helps :)