Question

How do you simplify `(7+5i)(7-5i)` and write the complex number in standard form?

Answer 1

`(7+5i)(7-5i)=74+i0`

Explanation:

Using the identity `(a+b)(a-b)=a^2-b^2`

`(7+5i)(7-5i)`

= `7^2-(5i)^2`

= `49-25i^2` - but `i^2=-1`

Hence this is `49-25xx(-1)=49+25=74`

and in standard form, this can be written as `74+i0`