Question

How do you simplify `8/(1+i)` and write the complex number in standard form?

Answer 1

`4 -4i`

Explanation:

Recall that we can multiply the top and bottom of a fraction by the same thing without changing the value of the fraction. In this case we will multiply by the complex conjugate of the complex number on the denominator.

For `z = 1+i` we have `bar(z) = 1 - i`

`8/(1+i) * (1-i)/(1-i) = (8-8i)/(1-i^2)`

Remember that `i^2 = -1` so we have

`(8-8i)/2 = 4 - 4i`