Initial program 30.3
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right) \cdot \log base + \tan^{-1}_* \frac{im}{re} \cdot 0}{\log base \cdot \log base + 0 \cdot 0}\]
Simplified0.4
\[\leadsto \color{blue}{\frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}}\]
- 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 pow10.4
\[\leadsto \frac{1}{\frac{\log base}{\log \color{blue}{\left({\left(\sqrt{re^2 + im^2}^*\right)}^{1}\right)}}}\]
Applied log-pow0.4
\[\leadsto \frac{1}{\frac{\log base}{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Applied *-un-lft-identity0.4
\[\leadsto \frac{1}{\frac{\color{blue}{1 \cdot \log base}}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}\]
Applied times-frac0.4
\[\leadsto \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{\log base}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Applied add-cube-cbrt0.4
\[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{\frac{1}{1} \cdot \frac{\log base}{\log \left(\sqrt{re^2 + im^2}^*\right)}}\]
Applied times-frac0.4
\[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\frac{1}{1}} \cdot \frac{\sqrt[3]{1}}{\frac{\log base}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Simplified0.4
\[\leadsto \color{blue}{1} \cdot \frac{\sqrt[3]{1}}{\frac{\log base}{\log \left(\sqrt{re^2 + im^2}^*\right)}}\]
Simplified0.4
\[\leadsto 1 \cdot \color{blue}{\frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}}\]
Final simplification0.4
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log base}\]
