\(\frac{e^{i \cdot \frac{1}{2}} \cdot \left(100 \cdot n\right)}{{\left(e^{\frac{1}{8}}\right)}^{\left(i \cdot i\right)}}\)
- Started with
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}}\]
25.8
- Applied taylor to get
\[100 \cdot \frac{{\left(1 + \frac{i}{n}\right)}^{n} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}\]
27.1
- Taylor expanded around 0 to get
\[100 \cdot \frac{\color{red}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}} \leadsto 100 \cdot \frac{\color{blue}{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right)} - 1}{\frac{i}{n}}\]
27.1
- Applied simplify to get
\[\color{red}{100 \cdot \frac{\left(\frac{1}{2} \cdot {i}^2 + \left(1 + i\right)\right) - 1}{\frac{i}{n}}} \leadsto \color{blue}{\left(\frac{1}{2} \cdot i + 1\right) \cdot \frac{i \cdot 100}{\frac{i}{n}}}\]
12.8
- Using strategy
rm 12.8
- Applied add-exp-log to get
\[\left(\frac{1}{2} \cdot i + 1\right) \cdot \color{red}{\frac{i \cdot 100}{\frac{i}{n}}} \leadsto \left(\frac{1}{2} \cdot i + 1\right) \cdot \color{blue}{e^{\log \left(\frac{i \cdot 100}{\frac{i}{n}}\right)}}\]
21.6
- Applied add-exp-log to get
\[\color{red}{\left(\frac{1}{2} \cdot i + 1\right)} \cdot e^{\log \left(\frac{i \cdot 100}{\frac{i}{n}}\right)} \leadsto \color{blue}{e^{\log \left(\frac{1}{2} \cdot i + 1\right)}} \cdot e^{\log \left(\frac{i \cdot 100}{\frac{i}{n}}\right)}\]
23.7
- Applied prod-exp to get
\[\color{red}{e^{\log \left(\frac{1}{2} \cdot i + 1\right)} \cdot e^{\log \left(\frac{i \cdot 100}{\frac{i}{n}}\right)}} \leadsto \color{blue}{e^{\log \left(\frac{1}{2} \cdot i + 1\right) + \log \left(\frac{i \cdot 100}{\frac{i}{n}}\right)}}\]
23.7
- Applied simplify to get
\[e^{\color{red}{\log \left(\frac{1}{2} \cdot i + 1\right) + \log \left(\frac{i \cdot 100}{\frac{i}{n}}\right)}} \leadsto e^{\color{blue}{\log \left(100 \cdot n\right) + \log \left(i \cdot \frac{1}{2} + 1\right)}}\]
22.6
- Applied taylor to get
\[e^{\log \left(100 \cdot n\right) + \log \left(i \cdot \frac{1}{2} + 1\right)} \leadsto e^{\left(\log n + \left(\log 100 + \frac{1}{2} \cdot i\right)\right) - \frac{1}{8} \cdot {i}^2}\]
16.9
- Taylor expanded around 0 to get
\[e^{\color{red}{\left(\log n + \left(\log 100 + \frac{1}{2} \cdot i\right)\right) - \frac{1}{8} \cdot {i}^2}} \leadsto e^{\color{blue}{\left(\log n + \left(\log 100 + \frac{1}{2} \cdot i\right)\right) - \frac{1}{8} \cdot {i}^2}}\]
16.9
- Applied simplify to get
\[e^{\left(\log n + \left(\log 100 + \frac{1}{2} \cdot i\right)\right) - \frac{1}{8} \cdot {i}^2} \leadsto \frac{n \cdot e^{\log 100}}{\frac{{\left(e^{\frac{1}{8}}\right)}^{\left(i \cdot i\right)}}{e^{\frac{1}{2} \cdot i}}}\]
2.4
- Applied final simplification
- Applied simplify to get
\[\color{red}{\frac{n \cdot e^{\log 100}}{\frac{{\left(e^{\frac{1}{8}}\right)}^{\left(i \cdot i\right)}}{e^{\frac{1}{2} \cdot i}}}} \leadsto \color{blue}{\frac{e^{i \cdot \frac{1}{2}} \cdot \left(100 \cdot n\right)}{{\left(e^{\frac{1}{8}}\right)}^{\left(i \cdot i\right)}}}\]
2.1
