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    229. 

  229. <h1 id="cmath">cmath</h1>
    230. 

  230. <p>Mathematical functions for complex numbers.</p>
    231. 

  231. <p><a href="https://docs.python.org/3/library/cmath.html">https://docs.python.org/3/library/cmath.html</a></p>
    232. 

  232. <h4 id="source-code">Source code</h4>
    233. 

  233. <div id="source-code-code-1" class="codeblock-wrapper"><doc-codeblock>
    234. 

  234. <pre translate="no" class="language-python"><code v-pre class="language-python">import math
    235. 

  235. 

  236. class complex:
    237. 

  237.     def __init__(self, real, imag=0):
    238. 

  238.         self._real = float(real)
    239. 

  239.         self._imag = float(imag)
    240. 

  240. 

  241.     @property
    242. 

  242.     def real(self):
    243. 

  243.         return self._real
    244. 

  244. 

  245.     @property
    246. 

  246.     def imag(self):
    247. 

  247.         return self._imag
    248. 

  248. 

  249.     def conjugate(self):
    250. 

  250.         return complex(self.real, -self.imag)
    251. 

  251. 

  252.     def __repr__(self):
    253. 

  253.         s = ['(', str(self.real)]
    254. 

  254.         s.append('-' if self.imag &lt; 0 else '+')
    255. 

  255.         s.append(str(abs(self.imag)))
    256. 

  256.         s.append('j)')
    257. 

  257.         return ''.join(s)
    258. 

  258. 

  259.     def __eq__(self, other):
    260. 

  260.         if type(other) is complex:
    261. 

  261.             return self.real == other.real and self.imag == other.imag
    262. 

  262.         if type(other) in (int, float):
    263. 

  263.             return self.real == other and self.imag == 0
    264. 

  264.         return NotImplemented
    265. 

  265. 

  266.     def __ne__(self, other):
    267. 

  267.         res = self == other
    268. 

  268.         if res is NotImplemented:
    269. 

  269.             return res
    270. 

  270.         return not res
    271. 

  271. 

  272.     def __add__(self, other):
    273. 

  273.         if type(other) is complex:
    274. 

  274.             return complex(self.real + other.real, self.imag + other.imag)
    275. 

  275.         if type(other) in (int, float):
    276. 

  276.             return complex(self.real + other, self.imag)
    277. 

  277.         return NotImplemented
    278. 

  278. 

  279.     def __radd__(self, other):
    280. 

  280.         return self.__add__(other)
    281. 

  281. 

  282.     def __sub__(self, other):
    283. 

  283.         if type(other) is complex:
    284. 

  284.             return complex(self.real - other.real, self.imag - other.imag)
    285. 

  285.         if type(other) in (int, float):
    286. 

  286.             return complex(self.real - other, self.imag)
    287. 

  287.         return NotImplemented
    288. 

  288. 

  289.     def __rsub__(self, other):
    290. 

  290.         if type(other) is complex:
    291. 

  291.             return complex(other.real - self.real, other.imag - self.imag)
    292. 

  292.         if type(other) in (int, float):
    293. 

  293.             return complex(other - self.real, -self.imag)
    294. 

  294.         return NotImplemented
    295. 

  295. 

  296.     def __mul__(self, other):
    297. 

  297.         if type(other) is complex:
    298. 

  298.             return complex(self.real * other.real - self.imag * other.imag,
    299. 

  299.                            self.real * other.imag + self.imag * other.real)
    300. 

  300.         if type(other) in (int, float):
    301. 

  301.             return complex(self.real * other, self.imag * other)
    302. 

  302.         return NotImplemented
    303. 

  303. 

  304.     def __rmul__(self, other):
    305. 

  305.         return self.__mul__(other)
    306. 

  306. 

  307.     def __truediv__(self, other):
    308. 

  308.         if type(other) is complex:
    309. 

  309.             denominator = other.real ** 2 + other.imag ** 2
    310. 

  310.             real_part = (self.real * other.real + self.imag * other.imag) / denominator
    311. 

  311.             imag_part = (self.imag * other.real - self.real * other.imag) / denominator
    312. 

  312.             return complex(real_part, imag_part)
    313. 

  313.         if type(other) in (int, float):
    314. 

  314.             return complex(self.real / other, self.imag / other)
    315. 

  315.         return NotImplemented
    316. 

  316. 

  317.     def __pow__(self, other: int | float):
    318. 

  318.         if type(other) in (int, float):
    319. 

  319.             return complex(self.__abs__() ** other * math.cos(other * phase(self)),
    320. 

  320.                            self.__abs__() ** other * math.sin(other * phase(self)))
    321. 

  321.         return NotImplemented
    322. 

  322. 

  323.     def __abs__(self) -&gt; float:
    324. 

  324.         return math.sqrt(self.real ** 2 + self.imag ** 2)
    325. 

  325. 

  326.     def __neg__(self):
    327. 

  327.         return complex(-self.real, -self.imag)
    328. 

  328. 

  329.     def __hash__(self):
    330. 

  330.         return hash((self.real, self.imag))
    331. 

  331. 

  332. 

  333. # Conversions to and from polar coordinates
    334. 

  334. 

  335. def phase(z: complex):
    336. 

  336.     return math.atan2(z.imag, z.real)
    337. 

  337. 

  338. def polar(z: complex):
    339. 

  339.     return z.__abs__(), phase(z)
    340. 

  340. 

  341. def rect(r: float, phi: float):
    342. 

  342.     return r * math.cos(phi) + r * math.sin(phi) * 1j
    343. 

  343. 

  344. # Power and logarithmic functions
    345. 

  345. 

  346. def exp(z: complex):
    347. 

  347.     return math.exp(z.real) * rect(1, z.imag)
    348. 

  348. 

  349. def log(z: complex, base=2.718281828459045):
    350. 

  350.     return math.log(z.__abs__(), base) + phase(z) * 1j
    351. 

  351. 

  352. def log10(z: complex):
    353. 

  353.     return log(z, 10)
    354. 

  354. 

  355. def sqrt(z: complex):
    356. 

  356.     return z ** 0.5
    357. 

  357. 

  358. # Trigonometric functions
    359. 

  359. 

  360. def acos(z: complex):
    361. 

  361.     return -1j * log(z + sqrt(z * z - 1))
    362. 

  362. 

  363. def asin(z: complex):
    364. 

  364.     return -1j * log(1j * z + sqrt(1 - z * z))
    365. 

  365. 

  366. def atan(z: complex):
    367. 

  367.     return 1j / 2 * log((1 - 1j * z) / (1 + 1j * z))
    368. 

  368. 

  369. def cos(z: complex):
    370. 

  370.     return (exp(1j * z) + exp(-1j * z)) / 2
    371. 

  371. 

  372. def sin(z: complex):
    373. 

  373.     return (exp(1j * z) - exp(-1j * z)) / (2 * 1j)
    374. 

  374. 

  375. def tan(z: complex):
    376. 

  376.     return sin(z) / cos(z)
    377. 

  377. 

  378. # Hyperbolic functions
    379. 

  379. 

  380. def acosh(z: complex):
    381. 

  381.     return log(z + sqrt(z * z - 1))
    382. 

  382. 

  383. def asinh(z: complex):
    384. 

  384.     return log(z + sqrt(z * z + 1))
    385. 

  385. 

  386. def atanh(z: complex):
    387. 

  387.     return 1 / 2 * log((1 + z) / (1 - z))
    388. 

  388. 

  389. def cosh(z: complex):
    390. 

  390.     return (exp(z) + exp(-z)) / 2
    391. 

  391. 

  392. def sinh(z: complex):
    393. 

  393.     return (exp(z) - exp(-z)) / 2
    394. 

  394. 

  395. def tanh(z: complex):
    396. 

  396.     return sinh(z) / cosh(z)
    397. 

  397. 

  398. # Classification functions
    399. 

  399. 

  400. def isfinite(z: complex):
    401. 

  401.     return math.isfinite(z.real) and math.isfinite(z.imag)
    402. 

  402. 

  403. def isinf(z: complex):
    404. 

  404.     return math.isinf(z.real) or math.isinf(z.imag)
    405. 

  405. 

  406. def isnan(z: complex):
    407. 

  407.     return math.isnan(z.real) or math.isnan(z.imag)
    408. 

  408. 

  409. def isclose(a: complex, b: complex):
    410. 

  410.     return math.isclose(a.real, b.real) and math.isclose(a.imag, b.imag)
    411. 

  411. 

  412. # Constants
    413. 

  413. 

  414. pi = math.pi
    415. 

  415. e = math.e
    416. 

  416. tau = 2 * pi
    417. 

  417. inf = math.inf
    418. 

  418. infj = complex(0, inf)
    419. 

  419. nan = math.nan
    420. 

  420. nanj = complex(0, nan)</code></pre>
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  464.     <!-- Rendered if sidebar right is enabled -->
    465. 

  465.     <!-- Sidebar right skeleton-->
    466. 

  466.     <div v-cloak class="fixed top-0 bottom-0 right-0 translate-x-full bg-sidebar-right-bg border-sidebar-right-border lg:sticky lg:border-l lg:shrink-0 lg:pt-6 lg:translate-x-0 sm:w-1/2 lg:w-64 lg:z-0 md:w-104 sidebar-right skeleton">
    467. 

  467.         <div class="pl-5">
    468. 

  468.             <div class="w-32 h-3 mb-4 bg-skeleton-bg rounded-full loading"></div>
    469. 

  469.             <div class="w-48 h-3 mb-4 bg-skeleton-bg rounded-full loading"></div>
    470. 

  470.             <div class="w-40 h-3 mb-4 bg-skeleton-bg rounded-full loading"></div>
    471. 

  471.         </div>
    472. 

  472.     </div>
    473. 

  473. 

  474.     <!-- User should be able to hide sidebar right -->
    475. 

  475.     <doc-sidebar-right v-cloak></doc-sidebar-right>
    476. 

  476. </div>
    477. 

  477. 

  478.         </div>
    479. 

  479.     </div>
    480. 

  480. 

  481.     <doc-search-mobile></doc-search-mobile>
    482. 

  482.     <doc-back-to-top></doc-back-to-top>
    483. 

  483. </div>
    484. 

  484. 

  485. 

  486.     <div id="retype-overlay-target"></div>
    487. 

  487. 

  488.         <script data-cfasync="false">window.__DOCS__ = { "title": "cmath", level: 2, icon: "file", hasPrism: true, hasInstagram: false, hasMermaid: false, hasMath: false, tocDepth: 23, "md": "/modules/cmath.md" }</script>
    489. 

  489. </body>
    490. 

  490. </html>
    491.