Soo saarida xididka tiro kakan

Daabacaaddan, waxaan ku eegi doonaa sida aad xididka u yeelan karto tiro kakan, iyo sidoo kale sida tani ay gacan uga geysan karto xallinta isla'egyada afar geesoodka ah ee takoorkoodu ka yar yahay eber.

Soo saarida xididka tiro kakan

Xididka laba jibbaaran

Sida aan ognahay, suurtagal maaha in la qaato asalka tirada dhabta ah ee taban. Laakiin marka ay timaado tirooyinka adag, ficilkan waa la samayn karaa. Aynu ogaano.

Aynu nidhaahno waxaan haynaa lambar z = -9. Wixii √-9 waxaa jira laba xidid:

z₁ = √-9 = -3i

z₁ = √-9 = 3i

Aynu hubino natiijooyinka la helay anagoo xallinayna isla'egta z² = -9, iyada oo aan taas la iloobin i² = -1:

(-3i)² = (-3)² ⋅ i² = 9 ⋅ (-1) = -9

(3i)² = 3² ⋅ i² = 9 ⋅ (-1) = -9

Sidaa darteed, taas ayaanu ku caddaynay -3i и 3i waa xidid √-9.

Asalka lambarka taban waxaa badanaa loo qoraa sidan:

√-1 = ± i

√-4 = ± 2i

√-9 = ± 3i

√-16 = ± 4i iwm

Xididada awooda n

Ka soo qaad in nala siiyo isla'egyada foomka z = ⁿ√w… Waxeey heesataa n xididdada (z₀, of₁, of₂,…,z_n-1), kaas oo lagu xisaabin karo qaacidada hoose:

|w| waa moduleka tiro kakan w;

φ – dooddiisa

k waa halbeeg qaadata qiyamka: k = {0, 1, 2,…, n-1}.

Isla'egyada afar geesoodka ah ee xididada adag

Soo saarida xididka lambarka taban ayaa beddelaya fikradda caadiga ah ee uXNUMXbuXNUMXb. Haddii takoorid (D) waa in ka yar eber, ka dibna ma jiri karaan xidido dhab ah, laakiin waxay noqon karaan tirooyin adag.

Tusaale

Aynu xalino isla'egta x² - 8x + 20 = 0.

Solution

a = 1, b = -8, c = 20

D = b² - 4ac = 64 – 80 = -16

D <0, laakiin waxaan weli qaadan karnaa asalka takoorka taban:

√D = √-16 = ± 4i

Hadda waxaan xisaabin karnaa xididdada:

x_1,2 = (-b ± √D)/2a = (8 ± 4i)/2 = 4 ± 2i.

Sidaa darteed, isla'egta x² - 8x + 20 = 0 wuxuu leeyahay laba xidid oo isku dhafan oo isku dhafan:

x₁ = 4 + 2i

x₂ = 4 - 2i