化简 e^{pisqrt(2)(1+i)}

解答

化简

e^{π 2 (1 + i)}

e^{2 π} cos (2 π) + i e^{2 π} sin (2 π)

求解步骤

e^{π 2 (1 + i)}

使用虚数运算法则:

e^{a + ib} = e^{a} (cos (b) + i sin (b))

= e^{2 π} (cos (2 π) + i sin (2 π))

将

e^{2 π} (cos (2 π) + sin (2 π) i)

改写成标准复数形式:

e^{2 π} cos (2 π) + e^{2 π} sin (2 π) i

= e^{2 π} cos (2 π) + e^{2 π} sin (2 π) i

e x p an d \frac{248 ( 16 + 56 4 - 1 )}{15}

e x p an d so l v e (x^{2} + 4 x - 5)

e x p an d \frac{- 250 x ^{3} + 600 x ^{2} - 480 x + 129}{( 4 - 5 x ) ^{3}}

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

e x p an d (cosh (x) + sinh (x))^{3}