Initial program 30.7
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
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 div-inv0.4
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{1}{\sqrt{\log 10}}\right)}\]
- Using strategy
rm Applied add-cbrt-cube0.4
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \color{blue}{\sqrt[3]{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}}}\right)\]
Applied add-cbrt-cube0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \left(\color{blue}{\sqrt[3]{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}} \cdot \sqrt[3]{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}}\right)\]
Applied cbrt-unprod0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\sqrt[3]{\left(\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \left(\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{1}{\sqrt{\log 10}}\right) \cdot \frac{1}{\sqrt{\log 10}}\right)}}\]
Simplified0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \sqrt[3]{\color{blue}{\frac{{\left(\log \left(\sqrt{re^2 + im^2}^*\right)\right)}^{3}}{\log 10 \cdot \sqrt{\log 10}}}}\]
- Using strategy
rm Applied *-un-lft-identity0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \sqrt[3]{\frac{{\color{blue}{\left(1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right)}}^{3}}{\log 10 \cdot \sqrt{\log 10}}}\]
Applied unpow-prod-down0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \sqrt[3]{\frac{\color{blue}{{1}^{3} \cdot {\left(\log \left(\sqrt{re^2 + im^2}^*\right)\right)}^{3}}}{\log 10 \cdot \sqrt{\log 10}}}\]
Applied associate-/l*0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \sqrt[3]{\color{blue}{\frac{{1}^{3}}{\frac{\log 10 \cdot \sqrt{\log 10}}{{\left(\log \left(\sqrt{re^2 + im^2}^*\right)\right)}^{3}}}}}\]
Simplified0.6
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \sqrt[3]{\frac{\color{blue}{1}}{\frac{\log 10 \cdot \sqrt{\log 10}}{{\left(\log \left(\sqrt{re^2 + im^2}^*\right)\right)}^{3}}}}\]
Final simplification0.6
\[\leadsto \sqrt[3]{\frac{1}{\frac{\log 10 \cdot \sqrt{\log 10}}{{\left(\log \left(\sqrt{re^2 + im^2}^*\right)\right)}^{3}}}} \cdot \frac{1}{\sqrt{\log 10}}\]
