Question

负一的根号二次方等于多少

Answer 1

复变中
(-1)^(根号2) = e^(根号2*Ln(-1)) = e^(根号2 * (2kπ+ πi ))
e^(根号2) * (2k+1)πi
= cos(根号2(2k+1)π)+i sin(根号2(2k+1)π)
如果你取一个单值支,可以令k=0
得到 = cos(π根号2)+i sin(π根号2)