x^2+1=0
x=a+bi
a,b:R
(a+bi)^2+1=0
a^2+2abi-b^2+1=0
a^2-b^2+1+2abi=0
a^2-b^2+1=0
2ab=0
ab=0
a=0,orb=0
b^2=1
b=1orb=-1
b=0时,a^2=-1
无解
所以x=iorx=-i
x^2+1=0
x=a+bi
a,b:R
(a+bi)^2+1=0
a^2+2abi-b^2+1=0
a^2-b^2+1+2abi=0
a^2-b^2+1=0
2ab=0
ab=0
a=0,orb=0
b^2=1
b=1orb=-1
b=0时,a^2=-1
无解
所以x=iorx=-i