Initial program 31.3
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Initial simplification0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\]
- Using strategy
rm Applied *-un-lft-identity0.6
\[\leadsto \frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\log 10}\]
Applied associate-/l*0.6
\[\leadsto \color{blue}{\frac{1}{\frac{\log 10}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
- Using strategy
rm Applied pow10.6
\[\leadsto \frac{1}{\frac{\log 10}{\log \color{blue}{\left({\left(\sqrt{re^2 + im^2}^*\right)}^{1}\right)}}}\]
Applied log-pow0.6
\[\leadsto \frac{1}{\frac{\log 10}{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Applied add-sqr-sqrt0.6
\[\leadsto \frac{1}{\frac{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}\]
Applied times-frac0.8
\[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{\log 10}}{1} \cdot \frac{\sqrt{\log 10}}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Applied associate-/r*0.5
\[\leadsto \color{blue}{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\frac{\sqrt{\log 10}}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
- Using strategy
rm Applied div-inv0.6
\[\leadsto \frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\color{blue}{\sqrt{\log 10} \cdot \frac{1}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Applied associate-/r*0.4
\[\leadsto \color{blue}{\frac{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}}}{\frac{1}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
- Using strategy
rm Applied div-inv0.4
\[\leadsto \frac{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}}}{\color{blue}{1 \cdot \frac{1}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Applied add-sqr-sqrt0.4
\[\leadsto \frac{\color{blue}{\sqrt{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}}} \cdot \sqrt{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}}}}}{1 \cdot \frac{1}{\log \left(\sqrt{re^2 + im^2}^*\right)}}\]
Applied times-frac0.4
\[\leadsto \color{blue}{\frac{\sqrt{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}}}}{1} \cdot \frac{\sqrt{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}}}}{\frac{1}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
Simplified0.4
\[\leadsto \color{blue}{\sqrt{\frac{1}{\log 10}}} \cdot \frac{\sqrt{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}}}}{\frac{1}{\log \left(\sqrt{re^2 + im^2}^*\right)}}\]
Simplified0.4
\[\leadsto \sqrt{\frac{1}{\log 10}} \cdot \color{blue}{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \sqrt{\frac{1}{\log 10}}\right)}\]
Final simplification0.4
\[\leadsto \sqrt{\frac{1}{\log 10}} \cdot \left(\sqrt{\frac{1}{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right)\]
