Find the product or quotient. Write the answer in standard form.
-$$\frac { 7 - 8 i } { 7 + 4 i }$$
A) $\frac { 17 } { 65 } - \frac { 84 } { 65 } \mathrm { i }$
B) $\frac { 17 } { 33 } + \frac { 28 } { 11 } \mathrm { i }$
C) $\frac { 27 } { 11 } + \frac { 28 } { 11 } \mathrm { i }$
D) $\frac { 81 } { 65 } + \frac { 28 } { 65 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $7 + 4i$ is $7 - 4i$. Multiplying both the numerator and denominator by this conjugate, we get: $$\frac{(7 - 8i)(7 - 4i)}{(7 + 4i)(7 - 4i)} = \frac{49 - 28i - 56i + 32}{49 + 16} = \frac{81 - 84i}{65} = \frac{81}{65} - \frac{84}{65}i$$.

Find the Product or Quotient 7−8i7+4i\frac { 7 - 8 i } { 7 + 4 i }7+4i7−8i​

Find the Product or Quotient $\frac { 7 - 8 i } { 7 + 4 i }$