Initial program 31.4
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
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-frac0.6
\[\leadsto \color{blue}{\frac{1}{\sqrt{\log 10}} \cdot \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\sqrt{\log 10}}}\]
- Using strategy
rm Applied div-inv0.4
\[\leadsto \frac{1}{\sqrt{\log 10}} \cdot \color{blue}{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \frac{1}{\sqrt{\log 10}}\right)}\]
Applied associate-*r*0.4
\[\leadsto \color{blue}{\left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \frac{1}{\sqrt{\log 10}}}\]
- Using strategy
rm Applied add-sqr-sqrt0.4
\[\leadsto \left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \color{blue}{\left(\sqrt{\frac{1}{\sqrt{\log 10}}} \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}\right)}\]
Applied associate-*r*0.5
\[\leadsto \color{blue}{\left(\left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}\right) \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}}\]
- Using strategy
rm Applied add-sqr-sqrt0.5
\[\leadsto \left(\left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}\right) \cdot \sqrt{\color{blue}{\sqrt{\frac{1}{\sqrt{\log 10}}} \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}}}\]
Applied sqrt-prod0.6
\[\leadsto \left(\left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}\right) \cdot \color{blue}{\left(\sqrt{\sqrt{\frac{1}{\sqrt{\log 10}}}} \cdot \sqrt{\sqrt{\frac{1}{\sqrt{\log 10}}}}\right)}\]
Applied associate-*r*0.5
\[\leadsto \color{blue}{\left(\left(\left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}\right) \cdot \sqrt{\sqrt{\frac{1}{\sqrt{\log 10}}}}\right) \cdot \sqrt{\sqrt{\frac{1}{\sqrt{\log 10}}}}}\]
Final simplification0.5
\[\leadsto \left(\left(\left(\frac{1}{\sqrt{\log 10}} \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \sqrt{\frac{1}{\sqrt{\log 10}}}\right) \cdot \sqrt{\sqrt{\frac{1}{\sqrt{\log 10}}}}\right) \cdot \sqrt{\sqrt{\frac{1}{\sqrt{\log 10}}}}\]
