Answer
$$2\cdot\frac{i}{5+2i}=\frac{10i+4}{29}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2 \cdot \frac{i}{5+2i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2 \cdot \frac{2+5i}{29} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10i+4}{29}\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 5+2i \, $ to get $\,\, \dfrac{2+5i}{29} $. ( view steps ) |
| ② | Multiply $2$ by $ \dfrac{2+5i}{29} $ to get $ \dfrac{10i+4}{29} $. Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 2 \cdot \frac{2+5i}{29} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{2+5i}{29} \xlongequal{\text{Step 2}} \frac{ 2 \cdot \left( 2+5i \right) }{ 1 \cdot 29 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4+10i }{ 29 } = \frac{10i+4}{29} \end{aligned} $$ |
This page was created using
Complex Expression calculator