(exp(-phi*1i)*exp(-theta*1i))/4 + (exp(-phi*1i)*exp(theta*1i))/4 + (exp(phi*1i)*exp(-theta*1i))/4 + (exp(phi*1i)*exp(theta*1i))/4
时间: 2023-09-21 20:09:09 浏览: 89
对于这个式子,我们可以将每一项都利用欧拉公式将其化简,即:
(exp(-phi*1i)*exp(-theta*1i))/4 + (exp(-phi*1i)*exp(theta*1i))/4 + (exp(phi*1i)*exp(-theta*1i))/4 + (exp(phi*1i)*exp(theta*1i))/4
= ((cos(-phi) - i*sin(-phi))*(cos(-theta) - i*sin(-theta)) + (cos(-phi) - i*sin(-phi))*(cos(theta) + i*sin(theta)) + (cos(phi) + i*sin(phi))*(cos(-theta) - i*sin(-theta)) + (cos(phi) + i*sin(phi))*(cos(theta) + i*sin(theta)))/4
= ((cos(-phi)*cos(-theta) + sin(phi)*sin(theta) + i*(sin(-phi)*cos(-theta) - cos(-phi)*sin(theta))) + (cos(-phi)*cos(theta) - sin(phi)*sin(theta) - i*(sin(-phi)*sin(theta) + cos(-phi)*cos(theta))) + (cos(phi)*cos(-theta) - sin(phi)*sin(theta) + i*(sin(phi)*cos(-theta) + cos(phi)*sin(theta))) + (cos(phi)*cos(theta) + sin(phi)*sin(theta) + i*(sin(phi)*sin(theta) - cos(phi)*cos(theta))))/4
= ((cos(phi)*cos(theta) - sin(phi)*sin(theta)) + i*(sin(phi)*cos(theta) + cos(phi)*sin(theta)) + (cos(phi)*cos(theta) + sin(phi)*sin(theta)) + i*(-sin(phi)*cos(theta) + cos(phi)*sin(theta)) + (cos(phi)*cos(theta) - sin(phi)*sin(theta)) + i*(sin(phi)*cos(theta) + cos(phi)*sin(theta)) + (cos(phi)*cos(theta) + sin(phi)*sin(theta)) + i*(-sin(phi)*cos(theta) - cos(phi)*sin(theta))))/4
= (2*cos(phi)*cos(theta) + 2*i*sin(phi)*cos(theta))/4
= (cos(phi)*cos(theta) + i*sin(phi)*cos(theta))/2
因此,原来的式子可以化简为(cos(phi)*cos(theta) + i*sin(phi)*cos(theta))/2。
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