Question

How do you simplify `(1+3i )/( 2+2i)`?

Answer 1

I found: `1+1/2i`

Explanation:

You need to change the denominator into a pure real number by multiplying and dividing by the complex conjugate of the denominator:
`(1+3i)/(2+2i)*(2-2i)/(2-2i)=` multiply :
`=(2-2i+6i-6i^2)/(4+4)=`
considering that: `i^2=-1`:
`=(2+4i+6)/8=`
`=(8+4i)/8=`
`=4(2+i)/8=`
`=(2+i)/2=1+1/2i`