Answer
$$276.46\cdot\frac{i}{150+276.46i}=\frac{6900i+12696}{16446}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}276.46 \cdot \frac{i}{150+276.46i}& \xlongequal{ }276.46 \cdot \frac{i}{150+276i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}276.46 \cdot \frac{46+25i}{16446} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6900i+12696}{16446}\end{aligned} $$ | |
| ① | Divide $ \, i \, $ by $ \, 150+276i \, $ to get $\,\, \dfrac{46+25i}{16446} $. ( view steps ) |
| ② | Multiply $276$ by $ \dfrac{46+25i}{16446} $ to get $ \dfrac{6900i+12696}{16446} $. Step 1: Write $ 276 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 276 \cdot \frac{46+25i}{16446} & \xlongequal{\text{Step 1}} \frac{276}{\color{red}{1}} \cdot \frac{46+25i}{16446} \xlongequal{\text{Step 2}} \frac{ 276 \cdot \left( 46+25i \right) }{ 1 \cdot 16446 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12696+6900i }{ 16446 } = \frac{6900i+12696}{16446} \end{aligned} $$ |
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