Answer
$$47-13i-(\frac{6815}{145}-\frac{1885}{145}i)=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}47-13i-(\frac{6815}{145}-\frac{1885}{145}i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}47-13i - \frac{ 6815 : \color{orangered}{ 145 } }{ 145 : \color{orangered}{ 145 }} - \frac{ 1885 : \color{orangered}{ 145 } }{ 145 : \color{orangered}{ 145 }} \cdot i \xlongequal{ } \\[1 em] & \xlongequal{ }47-13i-(\frac{47}{1}-\frac{13}{1}i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}47-13i-(47-13i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}47-13i-47+13i \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{47} -\cancel{13i} -\cancel{47}+ \cancel{13i} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}0\end{aligned} $$ | |
| ① | Divide both the top and bottom numbers by $ \color{orangered}{ 145 } $. |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 145 } $. |
| ③ | Remove 1 from denominator. |
| ④ | Remove 1 from denominator. |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 47-13i \right) = -47+13i $$ |
| ⑥ | Combine like terms: $$ \, \color{blue}{ \cancel{47}} \, \, \color{green}{ -\cancel{13i}} \, \, \color{blue}{ -\cancel{47}} \,+ \, \color{green}{ \cancel{13i}} \, = \color{blue}{0} $$ |
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