Write the expression in the standard form a + bi.
-$$\frac { 35 + 13 i } { 5 - 4 i }$$
A) $3 - 5 \mathrm { i }$
B) $3 + 5 \mathrm { i }$
C) $5 + 3 \mathrm { i }$
D) $5 - 3 \mathrm { i }$

Question

Quizplus · Accepted Answer

To write the expression in the standard form $a + bi$, we multiply the numerator and the denominator by the conjugate of the denominator. The conjugate of $5 - 4i$ is $5 + 4i$. So, we have:$$\frac{35 + 13i}{5 - 4i} \times \frac{5 + 4i}{5 + 4i} = \frac{(35 + 13i)(5 + 4i)}{25 + 16} = \frac{175 + 140i + 65i + 52i^2}{41} = \frac{175 + 205i - 52}{41} = \frac{123 + 205i}{41} = 3 + 5i.$$Thus, the expression in standard form is $3 + 5i$.

Write the Expression in the Standard Form a + Bi 35+13i5−4i\frac { 35 + 13 i } { 5 - 4 i }5−4i35+13i​

Write the Expression in the Standard Form a + Bi $\frac { 35 + 13 i } { 5 - 4 i }$