Initial program 30.7
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
Applied simplify0.4
\[\leadsto \color{blue}{\frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}}\]
- Using strategy
rm Applied div-inv0.4
\[\leadsto \color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{1}{\log base}}\]
- Using strategy
rm Applied add-log-exp0.7
\[\leadsto \color{blue}{\log \left(e^{\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{1}{\log base}}\right)}\]
Applied simplify0.7
\[\leadsto \log \color{blue}{\left({\left(\sqrt{re^2 + im^2}^*\right)}^{\left(\frac{1}{\log base}\right)}\right)}\]
- Using strategy
rm Applied add-cube-cbrt0.7
\[\leadsto \log \left({\color{blue}{\left(\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right) \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}}^{\left(\frac{1}{\log base}\right)}\right)\]
Applied unpow-prod-down0.8
\[\leadsto \log \color{blue}{\left({\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}^{\left(\frac{1}{\log base}\right)} \cdot {\left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}^{\left(\frac{1}{\log base}\right)}\right)}\]
Applied log-prod0.7
\[\leadsto \color{blue}{\log \left({\left(\sqrt[3]{\sqrt{re^2 + im^2}^*} \cdot \sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}^{\left(\frac{1}{\log base}\right)}\right) + \log \left({\left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}^{\left(\frac{1}{\log base}\right)}\right)}\]
Applied simplify0.6
\[\leadsto \color{blue}{\frac{\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}{\frac{\log base}{1 + 1}}} + \log \left({\left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}^{\left(\frac{1}{\log base}\right)}\right)\]
Applied simplify0.4
\[\leadsto \frac{\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}{\frac{\log base}{1 + 1}} + \color{blue}{\frac{\log \left(\sqrt[3]{\sqrt{re^2 + im^2}^*}\right)}{\log base}}\]
