1285/8-60i=10^6M^2

Lösung

\frac{1285}{8} - 60 i = 1 0^{6} M^{2}

M = \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} - \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i, M = - \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} + \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i

Schritte zur Lösung

\frac{1285}{8} - 60 i = 1 0^{6} M^{2}

Ersetze

M = x + y i

\frac{1285}{8} - 60 i = 1 0^{6} (x + y i)^{2}

Schreibe

1 0^{6} (x + y i)^{2}

um:

(1000000 x^{2} - 1000000 y^{2}) + 2000000 i x y

\frac{1285}{8} - 60 i = (1000000 x^{2} - 1000000 y^{2}) + 2000000 i x y

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

[\frac{1285}{8} = 1000000 x^{2} - 1000000 y^{2} - 60 = 2000000 x y]

[\frac{1285}{8} = 1000000 x^{2} - 1000000 y^{2} - 60 = 2000000 x y] : x = \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5}, x = - \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5}, y = - \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} y = \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}

Setze in

M = x + y i

ein

M = \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} - \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i, M = - \frac{257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}}{800 5} + \frac{3}{25 5 257 + 1600000 \frac{66049}{160000 0 ^{2}} + \frac{9}{2500000000}} i

x + y i = (1 - i)^{2}

\frac{1 + z}{1 - z} = 8 i - 5

\frac{1 + 2 z}{3 + 2 z} = i

\frac{- 1}{b + i} = \frac{1}{- b + i}

(x + y) + (x - y) \cdot i = 2 + 5 \cdot i