Kompleks o’zgaruvchili funksiyalar. Asosiy elementar funksiyalar.
Aytaylik D- C kompleks tekislikning to’plam qismi bo’lsin. D sohada aniqlangan kompleks funksiya deb, uchun ning kompleks sonni mos keltiruvchi akslantirish tushuniladi. Agar bo’lsa, u holda ni
Kabi ifodalash mumkin, bu yerda - yani funksiyaning haqiqiy qismi, - funksiyaning mavhum qismi.
Kompleks o’zgaruvchili ba’zi bir funksiyalarni keltiraylik:
ko’p ma’noli funksiya, unda son uchun to’plamdan mos ravishda cheksiz ko’p qiymat mos keladi.
Auditoriya topshirig’i
1.1.
bo’lsa, funksiya uchun haqiqiy va mavhum qismlarni ajrating.
c)![](data:image/png;base64,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)
yechish:
.
Mustaqil yechish uchun misollar
Berilgan funksiyalar uchun haqiqiy va mavhum qismlarni ajrating
1.2.
1.3. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAASCAIAAAA2bnI+AAAA+klEQVR4nMXPPQtFUBgH8Dsom0GyWWziI8jAZLOz+Qhikq9hQFllZxSr1SyTWClM3FNK98W9pFv3P5ye5znn1zkHWpbldinQNfZryXFclmVX5Bm2L0/mVaqq6vt+VVUEQYBWEIQkSdYtGIbHcfwoPc/L83xlIBiGNU2D47jjOGD+7c6+7xEE2dogCMCapmkYhlEUfZNFUdA0/Tgpy9IwjDiOIejp8I5kGGZru66TZRn8HEXRl5M7UpKktZ7nGTDLsiiKur1lR5qmuda6rvM8L4piXdfAu657IFmWBb8iSdK27WmaNE0Dc0VRDu5s23arh2F4f+RHeT7/kHcv7Gbc2mzNNgAAAABJRU5ErkJggg==)
1.4.
1.5. ![](data:image/png;base64,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)
1.6.
1.7 ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAUCAIAAABUPWcsAAADwklEQVR4nO1XWSjsURiXptwnyvpC0Y1iUIqaImmUeLE+kCUkhkYZhGbGmi3FAx5kmcJEliQeSB4wZSkPIltjSbJHimzZ7i+nTnPP/z8z3HG7uvkepu983znn+37fdv4jeH19NfuPSPCvHfhk+gQ829vbs7OzoaGhDg4Opt9mIvHgmZ+fT0tLOzk5KSkpyc3NheTx8XFwcDA+Pp73ivr6+svLy+Tk5L/r6fuIxbO/vz8xMbGwsNDe3p6fn+/n53d8fFxWVra5uanVasvLy7lXnJ+f9/T0fNRwYGCgRqMBMz4+jkjd3Nz4+PggzwKBSSXDHk5PTx8YGLC0tExMTCwoKAgLC4uLiysqKhodHW1qauLiub+/b21ttbCw+KhhAgYEE3K5/Orqqqqq6o8g/EYsHmSmv78/IyPDxsYGS09PTyQKTHh4uK+vL/f8jzcy0Ynl5eWIiAgTLyHE4snOzpbJZE5OTggbluvr60R+e3tbV1fHPR8cHDw1NUV4ZOnu7k5Xa25u/vLywj2F/uzs7Nzb24MhLFdWVtCrRIVaaGhoQFgbGxtRFNgmFotRNeiCkZGRoKAgw0ZZPNXV1WiY1NRUzAMsHx4ezN46pKurS6FQcD2ztbXFTnt7e6RxcXGRu4GXVCoVNhMwGDZoWjc3N6JC1Pr6+mpqaqRSKbAlJCSgXjIzM5VKZU5OzvT0tGGjPM1XW1uLAiA8qm5nZ+fw8LC4uBgZQ8sym2EMvzMzMxiAY2Nj78RzfX2NFiU8SsDV1RWZpCr4WllZKRQKz87OMId6e3vBI6ZPT09GjfLgubi4GBoaIvzz8/PPN7Kzs0NsuHhAu7u7hYWFGFN0NFHndHndwltdXYWLhEfsvLy8dFX+/v5Eu7GxQXkAo0d4jerF4+HhgV/yHeTi4kKEVlZWBwcH3M2YSygJVLm1tTUVUtf19Q+cxqQhPJrH29ubV7W2tsbL8xrViwdPwdbWlqOjI3jEgAiRa1Q5sxO+4t7S0lJ3d3fuPQYITkdGRlI8ZPZQFQkowUBTB3l0dLRRoywezJysrKy5uTmMlJaWlqioKCJHricnJ9F/kNPNeKAwfODN0dERDHR0dLwfDxqS4mHyExMTQ3i0VmxsLMUGE0aNsnicnZ27u7vz8vIkEgnalMoxcNra2pKSknQ3AzDeU3xGgMf7y/Wbt9iI0wEBAXhGKyoq0PQikWh4eJigYvKjy4eEhCwtLRk2ylNvaH21Ws0Ikffm5mZGiEeJ112jdHp6SpiUlBR9KhCgcuWGjX7/X/ja9I3na9MvL0kPxO2J2YMAAAAASUVORK5CYII=)
1.8
1.9. ![](data:image/png;base64,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)
1.10.
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