vereinfachen i(iz^3-2z)^6(3z^4-z^2+2z+iz^4)

Lösung

vereinfachen

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

(z^{22} + 36 z^{20} - 72 z^{18} - 480 z^{16} + 576 z^{12} + 24 z^{17} + 400 z^{14} - 320 z^{13} - 256 z^{10} + 384 z^{9}) + (- 3 z^{22} + 180 z^{18} - 720 z^{14} + 13 z^{20} + 192 z^{10} - 220 z^{16} + 432 z^{12} - 64 z^{8} - 2 z^{19} + 120 z^{15} - 480 z^{11} + 128 z^{7}) i

Schritte zur Lösung

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

Setze Klammern

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

Vereinfache

i (i z^{3} - 2 z)^{6} \cdot 3 z^{4} + i (i z^{3} - 2 z)^{6} (- z^{2}) + i (i z^{3} - 2 z)^{6} \cdot 2 z + i (i z^{3} - 2 z)^{6} i z^{4} : - 3 z^{22} i + z^{22} + 36 z^{20} + 180 z^{18} i - 72 z^{18} - 480 z^{16} - 720 z^{14} i + 576 z^{12} + 13 z^{20} i + 24 z^{17} + 400 z^{14} + 192 z^{10} i - 220 z^{16} i - 320 z^{13} + 432 z^{12} i - 256 z^{10} - 64 z^{8} i - 2 z^{19} i + 120 z^{15} i - 480 z^{11} i + 384 z^{9} + 128 z^{7} i

= - 3 z^{22} i + z^{22} + 36 z^{20} + 180 z^{18} i - 72 z^{18} - 480 z^{16} - 720 z^{14} i + 576 z^{12} + 13 z^{20} i + 24 z^{17} + 400 z^{14} + 192 z^{10} i - 220 z^{16} i - 320 z^{13} + 432 z^{12} i - 256 z^{10} - 64 z^{8} i - 2 z^{19} i + 120 z^{15} i - 480 z^{11} i + 384 z^{9} + 128 z^{7} i

Rewrite in standard complex form:

(z^{22} + 36 z^{20} - 72 z^{18} - 480 z^{16} + 576 z^{12} + 24 z^{17} + 400 z^{14} - 320 z^{13} - 256 z^{10} + 384 z^{9}) + (- 3 z^{22} + 180 z^{18} - 720 z^{14} + 13 z^{20} + 192 z^{10} - 220 z^{16} + 432 z^{12} - 64 z^{8} - 2 z^{19} + 120 z^{15} - 480 z^{11} + 128 z^{7}) i

= (z^{22} + 36 z^{20} - 72 z^{18} - 480 z^{16} + 576 z^{12} + 24 z^{17} + 400 z^{14} - 320 z^{13} - 256 z^{10} + 384 z^{9}) + (- 3 z^{22} + 180 z^{18} - 720 z^{14} + 13 z^{20} + 192 z^{10} - 220 z^{16} + 432 z^{12} - 64 z^{8} - 2 z^{19} + 120 z^{15} - 480 z^{11} + 128 z^{7}) i

s im pl i f y (x + 3 + x + 6) \cdot (x + 3)

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

e x p an d q (65 = \frac{300}{( q ^{2} + 9 ) ^{\frac{1}{2}}} + 74.25)

e x p an d 31

e x p an d (\frac{8 π}{3} - 43) c m^{2}