Równania liczb zespolonych

[marcinpruciak]

Czy tak?
\(\displaystyle{ z^{3} - 8i}\)
\(\displaystyle{ (z-2i)(z^{2} - 2iz + 4i)}\)
\(\displaystyle{ z1 = 2i}\)
\(\displaystyle{ del = 4i - 16}\)
\(\displaystyle{ z2 = \frac{2i - 2i - 4}{2} = -2}\)
\(\displaystyle{ z3 = \frac{2i+2i+4}{2} = 2i + 2}\)

x = z sprzężone
\(\displaystyle{ zx + (z - x) = 3 +2i}\)
\(\displaystyle{ (a+bi)(a-bi)+(a+bi)-(a-bi) = 3+2i}\)
\(\displaystyle{ (a^{2} = bi^{2})=(a+bi-a+bi) = 3 + 2i}\)
\(\displaystyle{ a^{2}+b^{2}+2bi = 3+2i}\)
\(\displaystyle{ a^{2}+b^{2}=3}\)
\(\displaystyle{ b=1 a= \sqrt{3}}\)

[szatkus]

\(\displaystyle{ \Delta = (-2i)^2-4*4i = -4-16i}\)

W drugim też już znalazłem błąd:

\(\displaystyle{ a^{2}+b^{2}+2bi = 3+2i \\
2bi = 2i\\
a^{2}+b^{2} = 3\\
b=1\\
a^{2}+1 = 3\\
a = \sqrt{2}}\)