solvefor x,y=-x^2+1graficar

Lösung

löse nach

x, y = - x^{2} + 1 g r a f i c a r

x = - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i

Schritte zur Lösung

y = - x^{2} + 1 \cdot g r a f i c a r

Ersetze

x = u + v i

y = - (u + v i)^{2} + 1 \cdot g r a f i c a r

Schreibe

- (u + v i)^{2} + 1 \cdot g r a f i c a r

um:

(- u^{2} + v^{2}) + i (- 2 uv + a^{2} c r^{2} f g)

y = (- u^{2} + v^{2}) + i (- 2 uv + a^{2} c r^{2} f g)

Schreibe

y

in der Standard komplexen Form um:

y + 0 i

y + 0 i = (- u^{2} + v^{2}) + i (- 2 uv + a^{2} c r^{2} f g)

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

[y = - u^{2} + v^{2} 0 = - 2 uv + a^{2} c r^{2} f g]

[y = - u^{2} + v^{2} 0 = - 2 uv + a^{2} c r^{2} f g] : u = - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, u = - - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, u = - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, u = - - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}, v = \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} v = - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} v = \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} v = - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}}

Setze in

x = u + v i

ein

x = - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y + a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} + \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i, x = - - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2} - \frac{a ^{2} c r ^{2} f g}{2 - \frac{y - a ^{4} c ^{2} r ^{4} f ^{2} g ^{2} + y ^{2}}{2}} i

z^{2} + 4 i = 0

\frac{1 - 2 i}{z} = (1 + i)^{2}

\frac{a + 2 i}{3 + bi} = 3

(a + bi) (x + y i) = 2 + 2 i

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