Questions: For the following exercise, evaluate the expression, writing the result as a simplified complex number. (1+2i)(2-2i)/(2-i)=□

Evaluate the expression \( \frac{(1+2i)(2-2i)}{2-i} \) and express the result as a simplified complex number.

Multiply the numerators \( (1+2i) \) and \( (2-2i) \).

Calculating the product gives \( (1)(2) + (1)(-2i) + (2i)(2) + (2i)(-2i) = 2 - 2i + 4i + 4 = 6 + 2i \).

Multiply the denominator \( (2-i) \) by its conjugate \( (2+i) \).

The product is \( (2)(2) + (2)(i) - (i)(2) - (i)(i) = 4 + 2i - 2i + 1 = 5 + 0i = 5 \).

Multiply the numerator product \( (6 + 2i) \) by the conjugate of the denominator \( (2 + i) \).

This gives \( (6)(2) + (6)(i) + (2i)(2) + (2i)(i) = 12 + 6i + 4i - 2 = 10 + 10i \).

Divide the final numerator \( (10 + 10i) \) by the denominator product \( (5) \).

This results in \( \frac{10 + 10i}{5} = 2 + 2i \).

The simplified complex number is \( \boxed{2 + 2i} \).

The result of the expression is \( \boxed{2 + 2i} \).