\(\frac{3}{1} \cdot \frac{\log \left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}{\log base}\)
- Started with
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
30.4
- Applied simplify to get
\[\color{red}{\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}} \leadsto \color{blue}{\frac{\log \left(\sqrt{im^2 + re^2}^*\right)}{\log base}}\]
0.4
- Using strategy
rm 0.4
- Applied add-cube-cbrt to get
\[\frac{\log \color{red}{\left(\sqrt{im^2 + re^2}^*\right)}}{\log base} \leadsto \frac{\log \color{blue}{\left({\left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}^3\right)}}{\log base}\]
0.4
- Using strategy
rm 0.4
- Applied *-un-lft-identity to get
\[\frac{\log \left({\left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}^3\right)}{\color{red}{\log base}} \leadsto \frac{\log \left({\left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}^3\right)}{\color{blue}{1 \cdot \log base}}\]
0.4
- Applied pow3 to get
\[\frac{\log \color{red}{\left({\left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}^3\right)}}{1 \cdot \log base} \leadsto \frac{\log \color{blue}{\left({\left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}^{3}\right)}}{1 \cdot \log base}\]
0.4
- Applied log-pow to get
\[\frac{\color{red}{\log \left({\left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}^{3}\right)}}{1 \cdot \log base} \leadsto \frac{\color{blue}{3 \cdot \log \left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}}{1 \cdot \log base}\]
0.4
- Applied times-frac to get
\[\color{red}{\frac{3 \cdot \log \left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}{1 \cdot \log base}} \leadsto \color{blue}{\frac{3}{1} \cdot \frac{\log \left(\sqrt[3]{\sqrt{im^2 + re^2}^*}\right)}{\log base}}\]
0.4
