Divide and express the result in standard form.
-$$\frac { 3 + 3 i } { 5 + 3 i }$$
A) $\frac { 12 } { 17 } + \frac { 3 } { 17 } \mathrm { i }$
B) $\frac { 3 } { 4 } + \frac { 3 } { 16 } \mathrm { i }$
C) $\frac { 6 } { 17 } - \frac { 24 } { 17 } \mathrm { i }$
D) $\frac { 3 } { 8 } + \frac { 3 } { 16 } \mathrm { i }$

Question

Quizplus · Accepted Answer

To divide complex numbers, you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of $5 + 3i$ is $5 - 3i$. Thus, $\frac{3 + 3i}{5 + 3i} \cdot \frac{5 - 3i}{5 - 3i} = \frac{15 - 9i + 15i - 9i^2}{25 - 9i^2}$. Since $i^2 = -1$, this simplifies to $\frac{15 + 6i + 9}{25 + 9} = \frac{24 + 6i}{34} = \frac{12}{17} + \frac{3}{17}i$.

Divide and Express the Result in Standard Form 3+3i5+3i\frac { 3 + 3 i } { 5 + 3 i }5+3i3+3i​

Divide and Express the Result in Standard Form $\frac { 3 + 3 i } { 5 + 3 i }$