Simplify by rationalizing the denominator. Write your answer in a +bi form.
-$\frac { 8 - 8 i } { 5 - 6 i }$
A) $- 8 + \frac { 8 } { 11 } \mathrm { i }$
B) $\frac { 8 } { 11 } + \frac { 8 } { 11 } \mathrm { i }$
C) $\frac { 88 } { 61 } + \frac { 8 } { 61 } \mathrm { i }$
D) $- \frac { 8 } { 61 } + \frac { 88 } { 61 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 8 - 8 i } { 5 - 6 i }$, multiply both the numerator and denominator by the conjugate of the denominator, which is $5 + 6i$. This gives: $\frac{(8 - 8i)(5 + 6i)}{(5 - 6i)(5 + 6i)}$. Simplifying, the numerator becomes $40 + 48i - 40i - 48i^2$ (since $i^2 = -1$), which simplifies to $40 + 8i + 48$, or $88 + 8i$. The denominator becomes $25 + 30i - 30i - 36i^2$, which simplifies to $25 + 36$, or $61$. Thus, the simplified form is $\frac{88 + 8i}{61}$, or $\frac{88}{61} + \frac{8}{61}i$.

Simplify by Rationalizing the Denominator 8−8i5−6i\frac { 8 - 8 i } { 5 - 6 i }5−6i8−8i​

Simplify by Rationalizing the Denominator $\frac { 8 - 8 i } { 5 - 6 i }$