Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\frac{56}{73}+\frac{21}{73}i& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-\frac{56}{73}+\frac{21i}{73} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{21i-56}{73}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{21}{73} $ by $ i $ to get $ \dfrac{ 21i }{ 73 } $. Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{21}{73} \cdot i & \xlongequal{\text{Step 1}} \frac{21}{73} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 21 \cdot i }{ 73 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 21i }{ 73 } \end{aligned} $$ |
| ② | Add $ \dfrac{-56}{73} $ and $ \dfrac{21i}{73} $ to get $ \dfrac{21i-56}{73} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{-56}{73} + \frac{21i}{73} & = \frac{-56}{\color{blue}{73}} + \frac{21i}{\color{blue}{73}} =\frac{ -56 + 21i }{ \color{blue}{ 73 }} = \\[1ex] &= \frac{21i-56}{73} \end{aligned} $$ |