Simplify the complex fraction 8i/(2-2i)?

We'll factorize the denominator by
2:

8i/2(1-i)

We'll simplify by
2:

4i/(1-i)

Since we are not
allowed to keep a complex number at denominator, this one has to be multiplied by it's
conjugate, which in this case is
(1+i).

4i/(1-i)=4i*(1+i)/(1-i)*(1+i)

(4i
+ 4i^2)/(1-i^2)

We know
that i^2=-1

Therefore, the number will
become:

(4i +
4i^2)/(1-i^2)=(4i-4)/(1+1)=4(-1+i)/2

We'll simplify and
we'll get:

4(-1+i)/2 = -2 +
2i

The simplified value of the given fraction
is: 8i/(2-2i) = -2 + 2i