Hfst 7: Complexe getallen gegeven door prof Willem Waegeman Deze samenvatting beslaat de cursus waaraan extra inzichten en bevindingen zijn toegevoegd + !!stappenplannen voor verschillende soorten oefeningen uit te werken!!
Vermenigvuldiging van 2 complexe getallen = product van moduli + som van de argumenten
z1z2 = r1r2(cos(θ1+θ2) + isin(θ1+θ2))
Stelling van de Moivre: zn = rn(cos(nθ) + isin(nθ))
Toepassing hierop is de n-de machtswortel berekenen
Bereken de n-de machtswortels van het complex getal z
Stel 𝑧 = 𝑤 𝑛
𝑛
√𝑧 = 𝑤 en gebruik bovenstaande formule dan om de n-de machtswortels te berekenen
Bereken r en θ0 en schrijf de formule met parameter k op
Als je n-wortels moet berekenen zal k = 0,1,2, ..., n-1
Vul ze allemaal eens in en zo bekom je de n-de machtswortels, werk uit om polaire vorm weg te werken
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