Question

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

Answer 1

It is

# ((1 + i)^2 + 2+2i)/ (2+i)=(1^2+2i+i^2+2+2i)/(2+i)= (4i+2)/(2+i)=2*(2i+1)/(2+i)=2*[(2i+1)*(2-i)]/[(2+i)*(2-i)]= 8/5+6i/5#

Remember that `i^2=-1`