Initial program 30.6
\[\frac{\log \left(\sqrt{re \cdot re + im \cdot im}\right)}{\log 10}\]
Initial simplification0.6
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\]
- Using strategy
rm Applied add-cbrt-cube1.5
\[\leadsto \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\color{blue}{\sqrt[3]{\left(\log 10 \cdot \log 10\right) \cdot \log 10}}}\]
Applied add-cbrt-cube1.3
\[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}}{\sqrt[3]{\left(\log 10 \cdot \log 10\right) \cdot \log 10}}\]
Applied cbrt-undiv0.7
\[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\log \left(\sqrt{re^2 + im^2}^*\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)\right) \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}{\left(\log 10 \cdot \log 10\right) \cdot \log 10}}}\]
Simplified0.7
\[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\log 10}\right)}^{3}}}\]
- Using strategy
rm Applied add-sqr-sqrt0.7
\[\leadsto \sqrt[3]{{\left(\frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\color{blue}{\sqrt{\log 10} \cdot \sqrt{\log 10}}}\right)}^{3}}\]
Applied *-un-lft-identity0.7
\[\leadsto \sqrt[3]{{\left(\frac{\color{blue}{1 \cdot \log \left(\sqrt{re^2 + im^2}^*\right)}}{\sqrt{\log 10} \cdot \sqrt{\log 10}}\right)}^{3}}\]
Applied times-frac0.7
\[\leadsto \sqrt[3]{{\color{blue}{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\sqrt{\log 10}}\right)}}^{3}}\]
Final simplification0.7
\[\leadsto \sqrt[3]{{\left(\frac{1}{\sqrt{\log 10}} \cdot \frac{\log \left(\sqrt{re^2 + im^2}^*\right)}{\sqrt{\log 10}}\right)}^{3}}\]
