vereinfachen (e^{iax})/((z+b)^2(z-b)^2)

Lösung

vereinfachen

\frac{e ^{ia x}}{( z + b ) ^{2} ( z - b ) ^{2}}

\frac{cos ( a x )}{b ^{4} + z ^{4} - 2 b ^{2} z ^{2}} + i \frac{sin ( a x )}{b ^{4} + z ^{4} - 2 b ^{2} z ^{2}}

Schritte zur Lösung

\frac{e ^{ia x}}{( z + b ) ^{2} ( z - b ) ^{2}}

e^{ia x} = cos (a x) + i sin (a x)

= \frac{cos ( a x ) + i sin ( a x )}{( z + b ) ^{2} ( z - b ) ^{2}}

Schreibe

\frac{cos ( a x ) + sin ( a x ) i}{( z + b ) ^{2} ( z - b ) ^{2}}

in der Standard komplexen Form um:

\frac{cos ( a x )}{z ^{4} - 2 b ^{2} z ^{2} + b ^{4}} + \frac{sin ( a x )}{z ^{4} - 2 b ^{2} z ^{2} + b ^{4}} i

= \frac{cos ( a x )}{z ^{4} - 2 b ^{2} z ^{2} + b ^{4}} + \frac{sin ( a x )}{z ^{4} - 2 b ^{2} z ^{2} + b ^{4}} i

e x p an d \frac{1}{( ( x - r ) ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}}

e x p an d \frac{1}{9 + 6 x}

e x p an d 1 + sin (b) (12, - 9)

e x p an d \frac{( x - 3 ) \cdot ( 25 \cdot x - 75 )}{2}

e x p an d \frac{1}{( t ^{2} - 9 ) ^{2}}