Find ${\left(-4+4i\right)}^2$ in two steps.

S1: Change all signs inside bracket.

S2: Apply formula

where $A=4$ and $B=4i$.

Combine like terms:

Multiply $\frac{1}{500}$ by $7+4i$ to get $\frac{4i+7}{500}$.

Step 1: Write $7+4i$ as a fraction by putting $1$ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

Multiply $\frac{4i+7}{500}$ by $-32i$ to get $\frac{-128i^2-224i}{500}$.

Step 1: Write $-32i$ as a fraction by putting $1$ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

Multiply $\frac{128-224i}{500}$ by $10+20i$ to get $\frac{-4480i^2+320i+1280}{500}$.

Step 1: Write $10+20i$ as a fraction by putting $1$ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

Simplify numerator