Initial program 31.1
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
Initial simplification0.4
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}\]
- Using strategy
rm Applied *-un-lft-identity0.4
\[\leadsto \frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\log base}\]
Applied associate-/l*0.4
\[\leadsto \color{blue}{\frac{1}{\frac{\log base}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
- Using strategy
rm Applied associate-/r/0.4
\[\leadsto \color{blue}{\frac{1}{\log base} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}\]
- Using strategy
rm Applied add-cube-cbrt0.4
\[\leadsto \frac{1}{\log base} \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}\]
Applied log-prod0.5
\[\leadsto \frac{1}{\log base} \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) + \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)\right)}\]
Applied distribute-lft-in0.5
\[\leadsto \color{blue}{\frac{1}{\log base} \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) + \frac{1}{\log base} \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}\]
Simplified0.4
\[\leadsto \frac{1}{\log base} \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) + \color{blue}{\frac{\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}{\log base}}\]
Final simplification0.4
\[\leadsto \frac{\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}{\log base} + \frac{1}{\log base} \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)\]
