Question
Answer
$$-\dfrac{1}{2}\cdot(1+i)\cdot2^{10}=\dfrac{1024i+1024}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\frac{1}{2}\cdot(1+i)\cdot2^{10}& \xlongequal{ }-\frac{1}{2}\cdot(1+i)\cdot1024 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{i+1}{2}\cdot1024 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1024i+1024}{2}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{1}{2} $ by $ 1+i $ to get $ \dfrac{i+1}{2} $. Step 1: Write $ 1+i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{1}{2} \cdot 1+i & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{1+i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot \left( 1+i \right) }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1+i }{ 2 } = \frac{i+1}{2} \end{aligned} $$ |
| ② | Multiply $ \dfrac{i+1}{2} $ by $ 1024 $ to get $ \dfrac{ 1024i+1024 }{ 2 } $. Step 1: Write $ 1024 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{i+1}{2} \cdot 1024 & \xlongequal{\text{Step 1}} \frac{i+1}{2} \cdot \frac{1024}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( i+1 \right) \cdot 1024 }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1024i+1024 }{ 2 } \end{aligned} $$ |
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