Question

s as a complex number in simplest a+bi form:
\frac{-1 - 23i}{-2 + 7i}

Explanation:

Step1: Multiply numerator and denominator by the conjugate of the denominator.

The conjugate of \(-2 + 7i\) is \(-2 - 7i\). So we have:

$$ \frac{(-1 - 23i)(-2 - 7i)}{(-2 + 7i)(-2 - 7i)} $$

Step2: Expand the numerator using the distributive property (FOIL method).

$$
LATEXBLOCK0
$$

Step3: Expand the denominator using the difference of squares formula \((a + b)(a - b)=a^{2}-b^{2}\).

$$
LATEXBLOCK1
$$

Step4: Divide the numerator by the denominator.

$$ \frac{-159 + 53i}{53}=\frac{-159}{53}+\frac{53i}{53}=-3 + i $$

Answer:

\(-3 + i\)