Question

Write the complex number `8/(1+i)` in standard form?

Answer 1

In the division of complex number you need first to change the denominator into a pure real number. To do that you multiply and divide by the complex conjugate of the denominator, in this case, `1-i`. So:

`8/(1+i)*(1-i)/(1-i)=(8-8i)/(1+1)=8/2-8/2i=4-4i`

Remember that: `(1+i)(1-i)=1-i+i-i^2` but `i^2=sqrt(-1))^2=-1`
giving: `(1+i)(1-i)=1+1=2`