vereinfachen (x^2+4i)^2

Lösung

vereinfachen

(x^{2} + 4 i)^{2}

(x^{4} - 16) + 8 x^{2} i

Schritte zur Lösung

(x^{2} + 4 i)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

(x^{2} + 4 i)^{2} = (x^{2})^{2} + 2 x^{2} \cdot 4 i + (4 i)^{2}

= (x^{2})^{2} + 2 x^{2} \cdot 4 i + (4 i)^{2}

(x^{2})^{2} = x^{4}

2 x^{2} \cdot 4 i = 8 x^{2} i

(4 i)^{2} = - 16

= x^{4} + 8 x^{2} i - 16

Rewrite in standard complex form:

(x^{4} - 16) + 8 x^{2} i

= (x^{4} - 16) + 8 x^{2} i

s im pl i f y (1 + cos (x)) (cos (x))

e x p an d 1 - sin (x) (1 + sin (x))

s im pl i f y (10 \frac{2465288}{2083583} - 1) \cdot 100

s im pl i f y (1 - sin (x)) (cos (x))

e x p an d a (x, - 1, - 1) + b (- 1, x, - 1) + c (- 1, - 1, x)