Chapter 11 - Additional Topics - 11.4 - Complex Numbers - Problem Set 11.4 - Page 493: 36

$42$

We start with the given expression: $(-6i)(7i)$ We regroup the real and imaginary terms using the associative and commutative properties of multiplication: $(-6\times7)(i\times i)$ We multiply the real and imaginary terms: $-42i^2$ Since $i^2$ is equal to $-1$, we simplify the expression as follows: $-42\times-1=42$