vereinfachen-2(z+i)^4-4(z+i)^3

Lösung

vereinfachen

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

- 2 ((z^{4} - 6 z^{2} + 1) + (4 z^{3} - 4 z) i) - 4 ((z^{3} - 3 z) + (3 z^{2} - 1) i)

Schritte zur Lösung

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

(z + i)^{4} = z^{4} + 4 i z^{3} - 6 z^{2} - 4 i z + 1

(z + i)^{3} = z^{3} + 3 z^{2} i - 3 z - i

= - 2 (z^{4} + 4 i z^{3} - 6 z^{2} - 4 i z + 1) - 4 (z^{3} + 3 z^{2} i - 3 z - i)

Rewrite in standard complex form:

- 2 ((z^{4} - 6 z^{2} + 1) + (4 z^{3} - 4 z) i) - 4 ((z^{3} - 3 z) + (3 z^{2} - 1) i)

= - 2 ((z^{4} - 6 z^{2} + 1) + (4 z^{3} - 4 z) i) - 4 ((z^{3} - 3 z) + (3 z^{2} - 1) i)

e x p an d p (3, - 1) Q (- 1, 5)

e x p an d sin (7 t) u (t - \frac{9 π}{14})

e x p an d (y^{4} + 2 x y^{4} - x^{3}) d x + (4 x y^{3} + 16 x^{2} y^{3}) d y

s im pl i f y (x + \frac{39 + 471}{5}) (x + \frac{39 - 471}{5})

e x p an d \frac{( x ^{4} - 4 x ^{3} + 4 x ^{2} )}{( x + 4 ) ^{5} \cdot ( 5 - x ) ^{3}}