Initial program 30.4
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Initial simplification0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\]
- Using strategy
rm Applied add-sqr-sqrt0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\]
Applied pow10.6
\[\leadsto \frac{\log \color{blue}{\left({\left(\sqrt{re^2 + im^2}^*\right)}^{1}\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]
Applied log-pow0.6
\[\leadsto \frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\]
Applied times-frac0.5
\[\leadsto \color{blue}{\frac{1}{\sqrt{\log 10}} \cdot \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\sqrt{\log 10}}}\]
- Using strategy
rm Applied *-un-lft-identity0.5
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\sqrt{\log 10}}\]
Applied associate-/l*0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\frac{1}{\frac{\sqrt{\log 10}}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
- Using strategy
rm Applied associate-/r/0.4
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right)}\]
Applied associate-*r*0.3
\[\leadsto \color{blue}{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}\]
Final simplification0.3
\[\leadsto \log \left(\sqrt{re^2 + im^2}^*\right) \cdot \left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right)\]
