vereinfachen (t+t^2i)^2

Lösung

vereinfachen

(t + t^{2} i)^{2}

(t^{2} - t^{4}) + 2 t^{3} i

Schritte zur Lösung

(t + t^{2} i)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(t + t^{2} i)^{2} = t^{2} + 2 t t^{2} i + (t^{2} i)^{2}

= t^{2} + 2 t t^{2} i + (t^{2} i)^{2}

2 t t^{2} i = 2 t^{3} i

(t^{2} i)^{2} = - t^{4}

= t^{2} + 2 t^{3} i - t^{4}

Rewrite in standard complex form:

(t^{2} - t^{4}) + 2 t^{3} i

= (t^{2} - t^{4}) + 2 t^{3} i

e x p an d (2 x y + 4 x^{3} y^{2}) d x + (3 x^{2} + 4 x^{4} y) d y

e x p an d (x^{2} - 81) y^{''} (x) + (9 - x) y^{'} (x) + (x^{2} + 18 x + 81) y

s im pl i f y (3 + i)^{10}

e x p an d e^{x} (- e^{- x} x - e^{- x})

e x p an d \frac{( 6 - 3 x ) ^{2}}{4}