解答
求解 x,sif=yx2−xy3
解答
x=2−8yy5+y10+16s2f2ysf+−8yy5+16s2f2+y10y3+−8yy5+16s2f2+y10i,x=−2−8yy5+y10+16s2f2ysf−−8yy5+16s2f2+y10y3−−8yy5+16s2f2+y10i,x=2−8yy5−y10+16s2f2ysf+−8yy5−16s2f2+y10y3+−8yy5−16s2f2+y10i,x=−2−8yy5−y10+16s2f2ysf−−8yy5−16s2f2+y10y3−−8yy5−16s2f2+y10i
求解步骤
sif=yx2−xy3
替代 x=a+bisif=y(a+bi)2−(a+bi)y3
展开 y(a+bi)2−(a+bi)y3:(ya2−yb2−y3a)+i(−y3b+2yab)
sif=(ya2−yb2−y3a)+i(−y3b+2yab)
将 sif 改写成标准复数形式:0+sfi0+sfi=(ya2−yb2−y3a)+i(−y3b+2yab)
复数仅在实部和虚部均相等时才相等改写为方程组:[0=ya2−yb2−y3asf=−y3b+2yab]
[0=ya2−yb2−y3asf=−y3b+2yab]:a=2−8yy5+y10+16s2f2ysf+−8yy5+16s2f2+y10y3,a=−2−8yy5+y10+16s2f2ysf−−8yy5+16s2f2+y10y3,a=2−8yy5−y10+16s2f2ysf+−8yy5−16s2f2+y10y3,a=−2−8yy5−y10+16s2f2ysf−−8yy5−16s2f2+y10y3,b=−8yy5+16s2f2+y10b=−−8yy5+16s2f2+y10b=−8yy5−16s2f2+y10b=−−8yy5−16s2f2+y10
x=a+bi代回x=2−8yy5+y10+16s2f2ysf+−8yy5+16s2f2+y10y3+−8yy5+16s2f2+y10i,x=−2−8yy5+y10+16s2f2ysf−−8yy5+16s2f2+y10y3−−8yy5+16s2f2+y10i,x=2−8yy5−y10+16s2f2ysf+−8yy5−16s2f2+y10y3+−8yy5−16s2f2+y10i,x=−2−8yy5−y10+16s2f2ysf−−8yy5−16s2f2+y10y3−−8yy5−16s2f2+y10i