vereinfachen (3(1-t)-it)^2

Lösung

vereinfachen

(3 (1 - t) - i t)^{2}

((3 (1 - t))^{2} - t^{2}) + (- 6 t + 6 t^{2}) i

Schritte zur Lösung

(3 (1 - t) - i t)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(3 (1 - t) - i t)^{2} = (3 (1 - t))^{2} - 2 \cdot 3 (1 - t) i t + (i t)^{2}

= (3 (1 - t))^{2} - 2 \cdot 3 (1 - t) i t + (i t)^{2}

- 2 \cdot 3 (1 - t) i t = - 6 t i (1 - t)

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

= (3 (1 - t))^{2} - 6 t i (1 - t) - t^{2}

Schreibe

- 6 t i (1 - t)

um:

- 6 t i + 6 t^{2} i

= (3 (1 - t))^{2} - 6 t i + 6 t^{2} i - t^{2}

Rewrite in standard complex form:

((3 (1 - t))^{2} - t^{2}) + (- 6 t + 6 t^{2}) i

= ((3 (1 - t))^{2} - t^{2}) + (- 6 t + 6 t^{2}) i

s im pl i f y (a + b)^{2} - 2 a b

e x p an d \frac{( x - 4 ) ( x + 6 )}{x}

e x p an d 2 (3 + 7)

e x p an d (- 4 - 6) d i rec t r i z

e x p an d (e^{\frac{x}{20}} - e^{- \frac{x}{20}})^{2}