express as a complex number in simplest a+bi form: $\frac{14 - 8i}{-6 - 4i}$

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by the conjugate of the denominator $- 6 + 4i$. $\frac{(14 - 8i)(-6 + 4i)}{(-6 - 4i)(-6 + 4i)}$

Step2: Expand numerator

Use FOIL method: $(14 - 8i)(-6 + 4i)=14\times(-6)+14\times4i-8i\times(-6)-8i\times4i=-84 + 56i+48i - 32i^{2}$. Since $i^{2}=-1$, it becomes $-84 + 56i+48i+32=-52 + 104i$.

Step3: Expand denominator

Use the difference - of - squares formula $(a + b)(a - b)=a^{2}-b^{2}$. Here $a=-6$ and $b = 4i$, so $(-6 - 4i)(-6 + 4i)=(-6)^{2}-(4i)^{2}=36-16i^{2}=36 + 16=52$.

Step4: Simplify the fraction

$\frac{-52 + 104i}{52}=\frac{-52}{52}+\frac{104i}{52}=-1 + 2i$.

Answer:

$-1 + 2i$