Aufgabe: z^4 -6z^2 +18=0
mein Versuch:
⇔ (z^2-3)^2 = -9 |√
⇔ z^2 -3 = 3i |+3 ∨ z^2 -3 = -3i | +3
⇔ z^2 = 3+3i ∨ z^2 = 3-3i
⇔ z^2 = √(18) e^(i(arctan(1) |√ ∨ z^2 = √(18) e^(i(2π-arctan(1) |√
⇔z_1 = 4^√(18) e^(i(arctan1)*(1/2)) ∨ z_2 = 4^√(18) e^(i(2π-arctan1)*(1/2))
⇔z_3 = 4^√(18) e^(i(2π+arctan1)*(1/2)) ∨ z_4= 4^√(18) e^(i(4π-arctan1)*(1/2))