Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{7+4 i}{8-4 i}$

A) $18+1 \mathrm{i}$

B) $\frac{3}{2}-\frac{1}{16} \mathrm{i}$

C) $\frac{1}{2}+\frac{3}{4} \mathrm{i}$

D) $\frac{1}{24}-\frac{1}{16} \mathrm{i}$

Question

Simplify by rationalizing the denominator. Write your answer in a + bi form.
-$\frac{7+4 i}{8-4 i}$

A) $18+1 \mathrm{i}$

B) $\frac{3}{2}-\frac{1}{16} \mathrm{i}$

C) $\frac{1}{2}+\frac{3}{4} \mathrm{i}$

D) $\frac{1}{24}-\frac{1}{16} \mathrm{i}$

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator: $(8+4i)$. This results in $\frac{(7+4i)(8+4i)}{(8-4i)(8+4i)}$. Simplifying gives $\frac{72+56i}{80}$, which reduces to $\frac{1}{2}+\frac{3}{4}i$.

Simplify by Rationalizing the Denominator 7+4i8−4i\frac{7+4 i}{8-4 i}8−4i7+4i​ A) 18+1i18+1 \mathrm{i}18+1i B) 32−116i\frac{3}{2}-\frac{1}{16} \mathrm{i}23​−161​i

Simplify by Rationalizing the Denominator $\frac{7+4 i}{8-4 i}$ A) $18+1 \mathrm{i}$ B) $\frac{3}{2}-\frac{1}{16} \mathrm{i}$