Question

Simplify 8 over the quantity of 2 plus 2i.

Answer 1

`(8)/(2+2i)=(8)/(2(1+i))=(4)/(1+i)=(4)/(1+i)\cdot(1-i)/(1-i)=(4(1+i))/(1^2-i^2)\\\\=(4(1+i))/(1-(-1))=(4(1+i))/(1+1)=(4(1+i))/(2)=2(1+i)=2+2i\\\\Used:\\(a-b)(a+b)=a^2-b^2\\\\i=√(-1)\to i^2=-1`