x+iy=(x-iy)^2

Lösung

x + i y = (x - i y)^{2}

x = 1, x = 0, x = - \frac{1}{2}, x = - \frac{1}{2}, y = 0 y = 0 y = \frac{3}{2} y = - \frac{3}{2}

Schritte zur Lösung

x + i y = (x - i y)^{2}

Schreibe

(x - i y)^{2}

um:

(x^{2} - y^{2}) - 2 i x y

x + i y = (x^{2} - y^{2}) - 2 i x y

Komplexe Zahlen können nur gleich sein wenn ihre realen und imaginären Teile gleich sind.Schreibe als Gleichungssystem um

[x = x^{2} - y^{2} y = - 2 x y]

[x = x^{2} - y^{2} y = - 2 x y] : x = 1, x = 0, x = - \frac{1}{2}, x = - \frac{1}{2}, y = 0 y = 0 y = \frac{3}{2} y = - \frac{3}{2}

x = 1, x = 0, x = - \frac{1}{2}, x = - \frac{1}{2}, y = 0 y = 0 y = \frac{3}{2} y = - \frac{3}{2}

so l v e f or x, x^{2} y + sin (y) = c

z^{2} - (5 + i) z + 8 + i = 0

4 i - 10 = 2 x + y i + 8

∣ 1 - (x + i y) ∣ = x + i y

4 x + (3 y + 4) i = 21 + 7 i