化简 (i(e^{-ipin}-1))/(pin)

解答

化简

\frac{i ( e ^{- iπn} - 1 )}{πn}

i \frac{( - 1 ) ^{n} - 1}{πn}

求解步骤

\frac{i ( e ^{- iπn} - 1 )}{πn}

i (e^{- iπn} - 1) = i (cos (- πn) + i sin (- πn) - 1)

= \frac{i ( cos ( - πn ) + i sin ( - πn ) - 1 )}{πn}

i (cos (- πn) + sin (- πn) i - 1) : i ((- 1)^{n} - 1)

= \frac{i ( ( - 1 ) ^{n} - 1 )}{πn}

将

\frac{( - 1 + ( - 1 ) ^{n} ) i}{πn}

改写成标准复数形式:

\frac{- 1 + ( - 1 ) ^{n}}{πn} i

= \frac{- 1 + ( - 1 ) ^{n}}{πn} i

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

e x p an d \frac{3 + x}{( x - 1 ) ( x + 2 )}

e x p an d \frac{s + b}{( s + a ) ( s ^{2} + cs + d )}

e x p an d \frac{( 0.2 + x ) ( x )}{0.4 - x}

e x p an d \frac{π ( 1 - x )}{1 + cos ( π x )}