1.7-bo'lim : Murakkab raqamlar
8. Ko'rsatilgan amalni bajaring va javobingizni standart shaklda yozing.
\[\frac{{1 + 5i}}{{ - 3i}}\]
Maslahat: Esda tutingki, standart shakl maxrajda \(i\) ga ruxsat bermaydi.
Yechim
Standart shakl \(i\) ning maxrajda bo'lishiga yo'l qo'ymagani uchun biz pay va maxrajni maxrajning konjugatiga, ya'ni \(3i\)ga ko'paytirishimiz kerak bo'ladi.
2-qadam
Konjugatga ko'paytirish,
\[\frac{{1 + 5i}}{{ - 3i}}\,\,\frac{{3i}}{{3i}} = \frac{{\left( {1 + 5i} \right)\left( {3i} \right)}}{{\left( { - 3i} \right)\left( {3i} \right)}}\]3-qadam
Endi biz qilishimiz kerak bo'lgan yagona narsa surat va maxrajdagi ko'paytirishni bajarish va natijani standart shaklga qo'yishdir.
\[\frac{{1 + 5i}}{{ - 3i}} = \frac{{3i + 15{i^2}}}{{ - 9{i^2}}} = \frac{{ - 15 + 3i}}{9} = - \frac{{15}}{9} + \frac{3}{9}i = \require{bbox} \bbox[2pt,border:1px solid black]{{ - \frac{5}{3} + \frac{1}{3}i}}\]