Write the quotient in standard form.
$\frac { 4 + i } { 4 - i }$
A) $\frac { 15 } { 17 }$ - $\frac { 8 } { 17 }$ i
B) $\frac { 15 } { 17 }$ + $\frac { 17 } { 8 }$ i
C) $\frac { 15 } { 17 }$ + $\frac { 8 } { 17 }$ i
D) $\frac { 17 } { 15 }$ + $\frac { 17 } { 8 }$ i
E) $\frac { 17 } { 15 }$ + $\frac { 8 } { 17 }$ i

Question

Write the quotient in standard form. 
 $\frac { 4 + i } { 4 - i }$  
A) $\frac { 15 } { 17 }$ - $\frac { 8 } { 17 }$ i
B) $\frac { 15 } { 17 }$ + $\frac { 17 } { 8 }$ i
C) $\frac { 15 } { 17 }$ + $\frac { 8 } { 17 }$ i
D) $\frac { 17 } { 15 }$ + $\frac { 17 } { 8 }$ i
E) $\frac { 17 } { 15 }$ + $\frac { 8 } { 17 }$ i

Quizplus · Accepted Answer

To simplify the given complex fraction $\frac { 4 + i } { 4 - i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $4 + i$. This results in $\frac{(4 + i)(4 + i)}{(4 - i)(4 + i)}$, simplifying to $\frac{16 + 8i + i^2}{16 - i^2}$. Since $i^2 = -1$, this further simplifies to $\frac{16 + 8i - 1}{16 + 1}$, which is $\frac{15 + 8i}{17}$, or $\frac{15}{17} + \frac{8}{17}i$, matching choice C.

Write the Quotient in Standard Form 4+i4−i\frac { 4 + i } { 4 - i }4−i4+i​

Write the Quotient in Standard Form $\frac { 4 + i } { 4 - i }$