Question
Answer
$$(-4+2i)\dfrac{-i}{-2-3i}=\dfrac{-2i-16}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-4+2i)\frac{-i}{-2-3i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-4+2i)\frac{3+2i}{13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4i^2-2i-12}{13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-4-2i-12}{13} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-2i-16}{13}\end{aligned} $$ | |
| ① | Divide $ \, -i \, $ by $ \, -2-3i \, $ to get $\,\, \dfrac{3+2i}{13} $. ( view steps ) |
| ② | Multiply $-4+2i$ by $ \dfrac{3+2i}{13} $ to get $ \dfrac{4i^2-2i-12}{13} $. Step 1: Write $ -4+2i $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} -4+2i \cdot \frac{3+2i}{13} & \xlongequal{\text{Step 1}} \frac{-4+2i}{\color{red}{1}} \cdot \frac{3+2i}{13} \xlongequal{\text{Step 2}} \frac{ \left( -4+2i \right) \cdot \left( 3+2i \right) }{ 1 \cdot 13 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -12-8i+6i+4i^2 }{ 13 } = \frac{4i^2-2i-12}{13} \end{aligned} $$ |
| ③ | $$ 4i^2 = 4 \cdot (-1) = -4 $$ |
| ④ | Simplify numerator $$ \color{blue}{-4} -2i \color{blue}{-12} = -2i \color{blue}{-16} $$ |
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