Write the expression in standard form.
-$$\frac { ( 1 + i ) ( 3 - i ) } { 2 + 3 i }$$
A) $\frac { 2 } { 13 } - \frac { 8 } { 13 } i$
B) $- \frac { 2 } { 5 } + \frac { 8 } { 5 } i$
C) $\frac { 14 } { 13 } - \frac { 8 } { 13 } \mathrm { i }$
D) $\frac { 14 } { 13 } + \frac { 8 } { 13 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To simplify the given expression, first multiply the numerators: $(1+i)(3-i) = 3 - i + 3i - i^2 = 3 + 2i + 1 = 4 + 2i$, since $i^2 = -1$. Then, to divide by the denominator $2+3i$, multiply the numerator and the denominator by the conjugate of the denominator: $(2-3i)$. This gives $(4+2i)(2-3i)/(2+3i)(2-3i)$. Simplifying, the numerator becomes $8 - 12i + 4i - 6i^2 = 8 - 8i + 6 = 14 - 8i$, and the denominator becomes $4 - 6i + 6i - 9i^2 = 4 + 9 = 13$. Thus, the expression in standard form is $(14 - 8i)/13$, which is $\frac{14}{13} - \frac{8}{13}i$.

Write the Expression in Standard Form (1+i)(3−i)2+3i\frac { ( 1 + i ) ( 3 - i ) } { 2 + 3 i }2+3i(1+i)(3−i)​

Write the Expression in Standard Form $\frac { ( 1 + i ) ( 3 - i ) } { 2 + 3 i }$