Kutora mudzi wenhamba yakaoma kunzwisisa

Muchinyorwa chino, tichatarisa kuti ungatora sei mudzi wenhamba yakaoma kunzwisisa, uyezve kuti izvi zvingabatsire sei mukugadzirisa quadratic equations ine rusarura rwuri pasi pe zero.

Kutora mudzi wenhamba yakaoma kunzwisisa

square root

Sezvatinoziva, hazvibviri kutora mudzi wenhamba chaiyo isina kunaka. Asi kana zvasvika kune nhamba dzakaoma, chiito ichi chinogona kuitwa. Ngatizvionei.

Ngatitii tine nhamba z = -9. For √-9 kune midzi miviri:

z₁ = √-9 = -3i

z₁ = √-9 = 3i

Ngatitarisei zvakawanikwa nekugadzirisa equation z² =-9, ndisingakanganwe izvozvo i² =-1:

(-3i)² = (-3)² ⋅ i² = 9 ⋅ (-1) = -9

(3i)² = 3² ⋅ i² = 9 ⋅ (-1) = -9

Nokudaro, takaratidza izvozvo -3i и 3i midzi √-9.

Midzi yenhamba isina kunaka inowanzonyorwa seizvi:

√-1 = ±i

√-4 = ±2i

√-9 = ±3i

√-16 = ±4i etc.

Mudzi kune simba re n

Ngatitii tapihwa maequation efomu z = ⁿ√w… Zvakadaro n midzi (z₀, of₁, of₂,…, z_n-1), iyo inogona kuverengerwa uchishandisa fomula pazasi:

|w| ndiyo module yenhamba yakaoma w;

φ - nharo yake

k ndiyo parameter inotora zvakakosha: k = {0, 1, 2,…, n-1}.

Quadratic equations ine midzi yakaoma

Kubvisa mudzi wenhamba yakaipa kunoshandura iyo yakajairwa pfungwa yeuXNUMXbuXNUMXb. Kana kusarura (D) iri pasi pe zero, saka hapagoni kuva nemidzi chaiyo, asi inogona kumiririrwa senhamba dzakaoma.

muenzaniso

Ngatigadzirise equation x² - 8x + 20 = 0.

mhinduro

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

D = b² – 4ac = 64 – 80 = -16

D <0, asi isu tinogona kutora mudzi wekusarura kwakashata:

√D = √-16 = ±4i

Iye zvino tinogona kuverenga midzi:

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

Naizvozvo, iyo equation x² - 8x + 20 = 0 ine miviri yakaoma conjugate midzi:

x₁ = 4 + 2i

x₂ = 4 – 2i