Question
Answer
$$2i\dfrac{6-4i}{3+3i}=\dfrac{10+2i}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2i\frac{6-4i}{3+3i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2i\frac{1-5i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-10i^2+2i}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10+2i}{3}\end{aligned} $$ | |
| ① | Divide $ \, 6-4i \, $ by $ \, 3+3i \, $ to get $\,\, \dfrac{1-5i}{3} $. ( view steps ) |
| ② | Multiply $2i$ by $ \dfrac{1-5i}{3} $ to get $ \dfrac{-10i^2+2i}{3} $. Step 1: Write $ 2i $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2i \cdot \frac{1-5i}{3} & \xlongequal{\text{Step 1}} \frac{2i}{\color{red}{1}} \cdot \frac{1-5i}{3} \xlongequal{\text{Step 2}} \frac{ 2i \cdot \left( 1-5i \right) }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2i-10i^2 }{ 3 } = \frac{-10i^2+2i}{3} \end{aligned} $$ |
| ③ | $$ -10i^2 = -10 \cdot (-1) = 10 $$ |
This page was created using
Complex Expression calculator