Multiply. Write the result in the form a + bi.
-$\left( \frac { 1 } { 3 } - \frac { 1 } { 2 } \mathrm { i } \right) \left( \frac { 3 } { 5 } - \frac { 3 } { 5 } \mathrm { i } \right)$
A) $- \frac { 13 } { 10 } - \frac { 33 } { 10 } \mathrm { i }$
B) $\frac { 1 } { 2 } - \frac { 1 } { 2 } \mathrm { i }$
C) $- \frac { 1 } { 10 } + \frac { 1 } { 2 } \mathrm { i }$
D) $- \frac { 1 } { 10 } - \frac { 1 } { 2 } i$

Question

Quizplus · Accepted Answer

To multiply the complex numbers, use the distributive property: $(\frac{1}{3} - \frac{1}{2}i)(\frac{3}{5} - \frac{3}{5}i) = \frac{1}{3} \cdot \frac{3}{5} - \frac{1}{3} \cdot \frac{3}{5}i - \frac{1}{2}i \cdot \frac{3}{5} + \frac{1}{2}i \cdot \frac{3}{5}i$. Simplifying, we get $\frac{1}{5} - \frac{1}{5}i - \frac{3}{10}i - \frac{3}{10}(-1)$. This results in $\frac{1}{5} + \frac{3}{10} - \frac{1}{5}i - \frac{3}{10}i = \frac{1}{5} + \frac{3}{10} - \frac{1}{2}i$. Converting to a common denominator, $\frac{1}{5} = \frac{2}{10}$, so $\frac{2}{10} + \frac{3}{10} = \frac{5}{10} = \frac{1}{2}$. Thus, the result is $\frac{1}{2} - \frac{1}{2}i$, which matches option D.

Multiply Write the Result in the Form a + Bi (13−12i)(35−35i)\left( \frac { 1 } { 3 } - \frac { 1 } { 2 } \mathrm { i } \right) \left( \frac { 3 } { 5 } - \frac { 3 } { 5 } \mathrm { i } \right)(31​−21​i)(53​−53​i)

Multiply Write the Result in the Form a + Bi $\left( \frac { 1 } { 3 } - \frac { 1 } { 2 } \mathrm { i } \right) \left( \frac { 3 } { 5 } - \frac { 3 } { 5 } \mathrm { i } \right)$