Initial program 30.8
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Initial simplification0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\]
- Using strategy
rm Applied pow10.6
\[\leadsto \frac{\log \color{blue}{\left({\left(\sqrt{re^2 + im^2}^*\right)}^{1}\right)}}{\log 10}\]
Applied log-pow0.6
\[\leadsto \frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\log 10}\]
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 add-exp-log0.6
\[\leadsto \frac{1}{\frac{\log 10}{\log \color{blue}{\left(e^{\log \left(\sqrt{re^2 + im^2}^*\right)}\right)}}}\]
Applied rem-log-exp0.6
\[\leadsto \frac{1}{\frac{\log 10}{\color{blue}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
- 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*0.6
\[\leadsto \color{blue}{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\frac{\sqrt{\log 10}}{\log \left(\sqrt{re^2 + im^2}^*\right)}}}\]
- Using strategy
rm Applied associate-/r/0.3
\[\leadsto \color{blue}{\frac{\frac{1}{\frac{\sqrt{\log 10}}{1}}}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}\]
Final simplification0.3
\[\leadsto \log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{\frac{1}{\sqrt{\log 10}}}{\sqrt{\log 10}}\]
