Write the expression in standard form.
-$$\frac { 1 + 3 i } { 5 + 4 i }$$
A) $\frac { 17 } { 9 } - \frac { 11 } { 9 } \mathrm { i }$
B) $\frac { 17 } { 41 } + \frac { 11 } { 41 } \mathrm { i }$
C) $- \frac { 7 } { 41 } - \frac { 19 } { 41 } i$
D) $- \frac { 7 } { 9 } - \frac { 11 } { 9 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To convert the given complex fraction to standard form, multiply the numerator and denominator by the conjugate of the denominator: $(5 + 4i)(5 - 4i) = 25 - 20i + 20i - 16i^2 = 25 + 16 = 41$. The numerator becomes $(1 + 3i)(5 - 4i) = 5 - 4i + 15i - 12i^2 = 5 + 11i + 12 = 17 + 11i$. Thus, the fraction simplifies to $\frac{17 + 11i}{41}$, which is option B.

Write the Expression in Standard Form 1+3i5+4i\frac { 1 + 3 i } { 5 + 4 i }5+4i1+3i​

Write the Expression in Standard Form $\frac { 1 + 3 i } { 5 + 4 i }$