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Kompleks sonlar ustida amallarni koʻrib chiqish

Kompleks sonlarni qoʻshish, ayirish va koʻpaytirishni koʻrib chiqing.
Qoʻshish
left parenthesis, a, start subscript, 1, end subscript, plus, b, start subscript, 1, end subscript, i, right parenthesis, plus, left parenthesis, a, start subscript, 2, end subscript, plus, b, start subscript, 2, end subscript, i, right parenthesis, equals, left parenthesis, a, start subscript, 1, end subscript, plus, a, start subscript, 2, end subscript, right parenthesis, plus, left parenthesis, b, start subscript, 1, end subscript, plus, b, start subscript, 2, end subscript, right parenthesis, i
Ayirish
left parenthesis, a, start subscript, 1, end subscript, plus, b, start subscript, 1, end subscript, i, right parenthesis, minus, left parenthesis, a, start subscript, 2, end subscript, plus, b, start subscript, 2, end subscript, i, right parenthesis, equals, left parenthesis, a, start subscript, 1, end subscript, minus, a, start subscript, 2, end subscript, right parenthesis, plus, left parenthesis, b, start subscript, 1, end subscript, minus, b, start subscript, 2, end subscript, right parenthesis, i
Koʻpaytirish
left parenthesis, a, start subscript, 1, end subscript, plus, b, start subscript, 1, end subscript, i, right parenthesis, dot, left parenthesis, a, start subscript, 2, end subscript, plus, b, start subscript, 2, end subscript, i, right parenthesis, equals, left parenthesis, a, start subscript, 1, end subscript, a, start subscript, 2, end subscript, minus, b, start subscript, 1, end subscript, b, start subscript, 2, end subscript, right parenthesis, plus, left parenthesis, a, start subscript, 1, end subscript, b, start subscript, 2, end subscript, plus, a, start subscript, 2, end subscript, b, start subscript, 1, end subscript, right parenthesis, i
Kompleks sonlar ustida amallar bajarish haqida koʻproq bilishni istaysizmi? Unda ushbu videolarni koʻring:

1–mashqlar toʻplami: Kompleks sonlarni qoʻshish va ayirish

1-misol: Kompleks sonlarni qoʻshish

Kompleks sonlarni qoʻshishda biz shunchaki haqiqiy va mavhum qismlarni qoʻshamiz. Masalan:
=(3+4i)+(610i)=(3+6)+(410)i=96i\begin{aligned} &\phantom{=}(\blueD 3+\greenD4i)+(\blueD6\greenD{-10}i) \\\\ &=(\blueD3+\blueD6)+(\greenD4\greenD{-10})i \\\\ &=\blueD9\greenD{-6}i \end{aligned}

2-misol: Kompleks sonlarni ayirish

Kompleks sonlarni ayirishda biz shunchaki haqiqiy qismdan mavhum qismni ayiramiz. Masalan:
=(3+4i)(610i)=(36)+(4(10))i=3+14i\begin{aligned} &\phantom{=}(\blueD 3+\greenD4i)-(\blueD6\greenD{-10}i) \\\\ &=(\blueD3-\blueD6)+(\greenD4-(\greenD{-10}))i \\\\ &=\blueD{-3}+\greenD{14}i \end{aligned}
1.1-masala
  • Joriy
left parenthesis, 7, minus, 10, i, right parenthesis, minus, left parenthesis, 3, plus, 30, i, right parenthesis, equals

Javobni left parenthesis, a, plus, b, i, right parenthesis koʻrinishida yozing.

Shu kabi misollarni koʻproq yechishni xohlaysizmi? Mashq.

2- mashqlar toʻplami: Kompleks sonlarni koʻpaytirish

Kompleks sonlarni koʻpaytirganda qavslarini ochish ikkihadlarni koʻpaytirish kabi ish koʻramiz:
left parenthesis, a, plus, b, right parenthesis, left parenthesis, c, plus, d, right parenthesis, equals, a, c, plus, a, d, plus, b, c, plus, b, d
Muntazam ikkihadlarni koʻpaytirishdan farqli oʻlaroq, kompleks sonlar uchun i, squared, equals, minus, 1 boʻlishini hisobga olamiz.

1-misol

=2(3+4i)=2(3)+24i=6+8i\begin{aligned} &\phantom{=}\blueD 2\cdot(\blueD{-3}+\greenD{4}i) \\\\ &=\blueD2\cdot(\blueD{-3})+\blueD2\cdot\greenD4i \\\\ &=\blueD{-6}+\greenD8i \end{aligned}

2-misol.

=3i(15i)=3i1+3i(5)i=3i15i2=3i15(1)=15+3i\begin{aligned} &\phantom{=}\greenD3i\cdot(\blueD{1}\greenD{-5}i) \\\\ &=\greenD3i\cdot\blueD1+\greenD3i\cdot(\greenD{-5})i \\\\ &=\greenD3i-15i^2 \\\\ &=\greenD3i-15(-1) \\\\ &=\blueD{15}+\greenD3i \end{aligned}

3-misol

=(2+3i)(15i)=21+2(5)i+3i1+3i(5)i=210i+3i15i2=27i15(1)=177i\begin{aligned} &\phantom{=}(\blueD2+\greenD3i)\cdot(\blueD{1}\greenD{-5}i) \\\\ &=\blueD2\cdot\blueD1+\blueD2\cdot(\greenD{-5})i+\greenD3i\cdot\blueD1+\greenD3i\cdot(\greenD{-5})i \\\\ &=\blueD2\greenD{-10}i+\greenD3i-15i^2 \\\\ &=\blueD2\greenD{-7}i-15(-1) \\\\ &=\blueD{17}\greenD{-7}i \end{aligned}
2.1-masala
  • Joriy
8, dot, left parenthesis, 11, i, plus, 2, right parenthesis, equals

Javobingiz a, plus, b, i kompleks son koʻrinishida boʻlishi kerak. Bu yerda a va b haqiqiy son.

Shu kabi misollarni koʻproq yechishni istaysizmi? Koʻring bu asosiy mashq va bu rivojlangan mashq.