{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2026-02-17T06:10:37.823863Z",
     "start_time": "2026-02-17T06:10:37.590164Z"
    }
   },
   "source": [
    "def abs(c):\n",
    "    return (c.real**2 + c.imag**2)**0.5\n",
    "\n",
    "def add(c1, c2):\n",
    "    return complex(c1.real + c2.real, c1.imag + c2.imag)\n",
    "\n",
    "def sub(c1, c2):\n",
    "    # (a+bi) - (c+di) = (a-c) + (b-d)i\n",
    "    return complex(c1.real - c2.real, c1.imag - c2.imag)\n",
    "\n",
    "def mul(c1, c2):\n",
    "    # (a+bi)(c+di) = (ac-bd) + (ad+bc)i\n",
    "    return complex(c1.real * c2.real - c1.imag * c2.imag, c1.real * c2.imag + c1.imag * c2.real)\n",
    "\n",
    "\n",
    "\n",
    "print(mul(1+2j, 2+1j))"
   ],
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5j\n"
     ]
    }
   ],
   "execution_count": 1
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "9169fa196cc5ca5d"
  }
 ],
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