## 2019年10月28日月曜日

### 数学 - Python - 解析学 - “ε-δ”その他 - 複素数 - 定義 - 共役、商、絶対値、共役の共役

1. $\begin{array}{l}\left|\frac{\stackrel{-}{\alpha }}{\alpha }\right|\\ =\left|\frac{{\left(\stackrel{-}{\alpha }\right)}^{2}}{\alpha \stackrel{-}{\alpha }}\right|\\ =\frac{\left|{\left(\stackrel{-}{\alpha }\right)}^{2}\right|}{{\left|\alpha \right|}^{2}}\\ =\frac{{\left|\stackrel{-}{\alpha }\right|}^{2}}{{\left|\alpha \right|}^{2}}\\ =1\end{array}$

また、

$\stackrel{-}{\stackrel{-}{\alpha }}=\alpha$

コード

Python 3

#!/usr/bin/env python3
from unittest import TestCase, main
from sympy import pprint, symbols

print('3.')

a = symbols('a', imag=True, nonzero=True)

class MyTestCase(TestCase):
def test1(self):
self.assertEqual(abs(a / a.conjugate()), 1)

def test2(self):
self.assertEqual(a.conjugate().conjugate(), a)

if __name__ == '__main__':
main()


% ./sample3.py -v
3.
test1 (__main__.MyTestCase) ... ok
test2 (__main__.MyTestCase) ... ok

----------------------------------------------------------------------
Ran 2 tests in 0.001s

OK
%