Question
Answer
$$\dfrac{3+5i}{3-5i}+\dfrac{3-5i}{3+5i}=-\dfrac{16}{17}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3+5i}{3-5i}+\frac{3-5i}{3+5i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-8+15i}{17}+\frac{-8-15i}{17} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{16}{17}\end{aligned} $$ | |
| ① | Divide $ \, 3+5i \, $ by $ \, 3-5i \, $ to get $\,\, \dfrac{-8+15i}{17} $. ( view steps )Divide $ \, 3-5i \, $ by $ \, 3+5i \, $ to get $\,\, \dfrac{-8-15i}{17} $. ( view steps ) |
| ② | Add $ \dfrac{-8+15i}{17} $ and $ \dfrac{-8-15i}{17} $ to get $ \dfrac{-16}{17} $. To add expressions with the same denominators, we add the numerators and write the result over the common denominator. $$ \begin{aligned} \frac{-8+15i}{17} + \frac{-8-15i}{17} & = \frac{-8+15i}{\color{blue}{17}} + \frac{-8-15i}{\color{blue}{17}} = \\[1ex] &=\frac{ -8+15i + \left( -8-15i \right) }{ \color{blue}{ 17 }}= \frac{-16}{17} \end{aligned} $$ |
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