Question
Answer
$$(x+iy)\cdot\dfrac{1}{26-52i}=\dfrac{iy+x}{-52i+26}$$
Explanation
| $$ \begin{aligned}(x+iy)\cdot\frac{1}{26-52i}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{iy+x}{-52i+26}\end{aligned} $$ | |
| ① | Multiply $x+iy$ by $ \dfrac{1}{26-52i} $ to get $ \dfrac{iy+x}{-52i+26} $. Step 1: Write $ x+iy $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} x+iy \cdot \frac{1}{26-52i} & \xlongequal{\text{Step 1}} \frac{x+iy}{\color{red}{1}} \cdot \frac{1}{26-52i} \xlongequal{\text{Step 2}} \frac{ \left( x+iy \right) \cdot 1 }{ 1 \cdot \left( 26-52i \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x+iy }{ 26-52i } = \frac{iy+x}{-52i+26} \end{aligned} $$ |
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