Problem:
Simplify the following expression $\left(-\frac{5}{3} \left(\cos \left(\frac{\pi }{45}\right)+i \sin \left(\frac{\pi }{45}\right)\right)\right)^4$
Answer:
$\frac{625}{81} \left(\cos \left(\frac{4 \pi }{45}\right)+i \sin \left(\frac{4 \pi }{45}\right)\right)$
{'source': 'AMPS', 'file': 'amps/mathematica/algebra/complex_raised_to_exponent/10829.txt'}