Problem:
Find the norm and argument (phase angle in radians) of $-2 \left(-\frac{1}{4}+\frac{\sqrt{5}}{4}+i \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}\right)$.
Answer:
Norm: $2 \sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}+\left(\frac{\sqrt{5}}{4}-\frac{1}{4}\right)^2}$
Argument: $-\pi -\tan ^{-1}\left(\frac{\sqrt{\frac{5}{8}+\frac{\sqrt{5}}{8}}}{\frac{1}{4}-\frac{\sqrt{5}}{4}}\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/complex_norm_and_arg/8200.txt'}