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 $\frac { 4 + i } { 4 - i }$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $4 + i$. This results in $\frac{(4+i)(4+i)}{(4-i)(4+i)}$, which simplifies to $\frac{16+8i+i^2}{16-i^2}$. Since $i^2 = -1$, this further simplifies to $\frac{16+8i-1}{16+1}$, or $\frac{15+8i}{17}$, which in standard form is $\frac{15}{17} + \frac{8}{17}i$.

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

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