Multiply $\frac{81}{145}$ by $i$ to get $\frac{81i}{145}$.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

Subtract $\frac{81i}{145}$ from $\frac{43}{145}$ to get $\frac{-81i+43}{145}$.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

Multiply $53+56i$ by $\frac{-81i+43}{145}$ to get $\frac{-4536i^2-1885i+2279}{145}$.

Step 1: Write $53+56i$ as a fraction by putting $1$ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

Simplify numerator