vereinfachen ((2-3i)^2-(2+3i)(3-2i))/(3i^{17)-1}-4/(5i^{-25)}

Lösung

vereinfachen

\frac{( 2 - 3 i ) ^{2} - ( 2 + 3 i ) ( 3 - 2 i )}{3 i ^{17} - 1} - \frac{4}{5 i ^{- 25}}

- \frac{17}{5} + 6 i

Schritte zur Lösung

\frac{( 2 - 3 i ) ^{2} - ( 2 + 3 i ) ( 3 - 2 i )}{3 i ^{17} - 1} - \frac{4}{5 i ^{- 25}}

\frac{( 2 - 3 i ) ^{2} - ( 2 + 3 i ) ( 3 - 2 i )}{3 i ^{17} - 1} = \frac{17 ( - 1 + 2 i )}{5}

\frac{4}{5 i ^{- 25}} = \frac{4 i}{5}

= \frac{17 ( - 1 + 2 i )}{5} - \frac{4 i}{5}

Füge zusammen:

\frac{17 ( - 1 + 2 i )}{5} - \frac{4 i}{5} : \frac{17 ( - 1 + 2 i ) - 4 i}{5}

= \frac{17 ( - 1 + 2 i ) - 4 i}{5}

Schreibe

17 (- 1 + 2 i) - 4 i

um:

- 17 + 30 i

= \frac{- 17 + 30 i}{5}

Wende Bruchregel an:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{- 17}{5} + \frac{30}{5} i

Vereinfache

\frac{- 17}{5} + \frac{30}{5} i : - \frac{17}{5} + 6 i

= - \frac{17}{5} + 6 i

s im pl i f y \frac{14}{15} - \frac{1}{6}

s im pl i f y (2 x)^{0}

f a c t or 2 x^{3} - 16 x^{2} - 18 x

w^{2} - 5 w - 6 = 0

∣ x + 4 ∣ = ∣ 3 x + 2 ∣