Question

1. if a = -3 + 5i, b = 4 - 2i, and c = 1 + 6i, where i is the imaginary unit, then a - bc equals. use parentheses
2. which expression is equivalent to (-2xki - 3)² - 5i³, where i is the imaginary unit?

Explanation:

Step1: Calculate \( BC \)

First, we need to multiply the complex numbers \( B = 4 - 2i \) and \( C = 1 + 6i \). Using the distributive property (FOIL method) for complex numbers:

$$
LATEXBLOCK0
$$

Since \( i^{2}=-1 \), we substitute that in:

$$
LATEXBLOCK1
$$

Step2: Calculate \( A - BC \)

Now, we subtract \( BC \) from \( A \), where \( A = -3 + 5i \):

$$
LATEXBLOCK2
$$

Using parentheses as required, we can write it as \( (-3 + 5i) - (4 - 2i)(1 + 6i) \) and after calculation, the result is \( (-19 - 17i) \).

Answer:

\((-3 + 5i) - (4 - 2i)(1 + 6i) = -19 - 17i\) (or in the form with parentheses as \((-19) + (-17)i\) if needed, but the simplified form is \(-19 - 17i\))