Divide and simplify to the form $a+b i$.
-$\frac{7-6 i}{5-8 i}$
A) $\frac{83}{89}+\frac{26}{89} \mathrm{i}$
B) $-\frac{13}{89}+\frac{86}{89} \mathrm{i}$
C) $-\frac{83}{39}+\frac{2}{3} \mathrm{i}$
D) $\frac{1}{3}+\frac{2}{3} \mathrm{i}$

Question

Quizplus · Accepted Answer

To simplify $\frac{7-6i}{5-8i}$, multiply both the numerator and denominator by the conjugate of the denominator, which is $5+8i$. This results in $\frac{(7-6i)(5+8i)}{(5-8i)(5+8i)}$, simplifying to $\frac{35+56i-30i-48i^2}{25-64i^2}$, which further simplifies to $\frac{83+26i}{89}$, or $\frac{83}{89}+\frac{26}{89}i$.

Divide and Simplify to the Form a+bia+b ia+bi - 7−6i5−8i\frac{7-6 i}{5-8 i}5−8i7−6i​

Divide and Simplify to the Form $a+b i$
- $\frac{7-6 i}{5-8 i}$