Initial program 31.4
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
Initial simplification0.4
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}\]
- Using strategy
rm Applied add-log-exp0.7
\[\leadsto \color{blue}{\log \left(e^{\frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}}\right)}\]
- Using strategy
rm Applied div-inv0.7
\[\leadsto \log \left(e^{\color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{1}{\log base}}}\right)\]
Applied exp-to-pow0.7
\[\leadsto \log \color{blue}{\left({\left(\sqrt{re^2 + im^2}^*\right)}^{\left(\frac{1}{\log base}\right)}\right)}\]
Applied log-pow0.4
\[\leadsto \color{blue}{\frac{1}{\log base} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}\]
- 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
\[\leadsto \frac{\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}{\log base} + \frac{1}{\log base} \cdot \log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)\]
