Question

How do you simplify `5/(1+i)`?

Answer 1

THe answer is `=5/2(1-i)`

Explanation:

To simplify a quotient, you must multiply the numerator and denominator by the conjugate of the denominator.

If a complex number is `z=a+ib` the the conjugate is `barz=a-ib`
Then `z*barz=(a+ib)(a-ib)=a^2-i^2b^2=a^2+b^2` as `i^2=-1`

sSo here, `5/(1+i)=(5(1-i))/((1+i)(1-i))=(5(1-i))/(1+1)=5/2(1-i)`