해법
25x2+60x+37=0a+bia+bi
해법
x=50−50−1+b2+1+a2b2+2ab2b+ab−60−50−1+b2+a2b2+2ab2+1+−50−1+b2+a2b2+2ab2+1i,x=−50−50−1+b2+1+a2b2+2ab2b+ab+60−50−1+b2+a2b2+2ab2+1−−50−1+b2+a2b2+2ab2+1i,x=521+b2+1+a2b2+2ab2b+ab−62b2+a2b2+2ab2+1+1+52b2+a2b2+2ab2+1+1i,x=−521+b2+1+a2b2+2ab2b+ab+62b2+a2b2+2ab2+1+1−52b2+a2b2+2ab2+1+1i
솔루션 단계
25x2+60x+37=0⋅a+bia+bi
대체 x=u+vi25(u+vi)2+60(u+vi)+37=0⋅a+bia+bi
확대되다
(25u2−25v2+60u+37)+i(60v+50uv)=i(b+ab)
다시 쓰다 i(b+ab) 표준복합형태로: 0+(b+ab)i(25u2−25v2+60u+37)+i(60v+50uv)=0+(b+ab)i
복소수는 실수 부분과 허수 부분이 같을 때만 같을 수 있다방정식으로 다시 쓰시오:[25u2−25v2+60u+37=060v+50uv=b+ab]
[25u2−25v2+60u+37=060v+50uv=b+ab]:u=50−50−1+b2+1+a2b2+2ab2b+ab−60−50−1+b2+a2b2+2ab2+1,u=−50−50−1+b2+1+a2b2+2ab2b+ab+60−50−1+b2+a2b2+2ab2+1,u=521+b2+1+a2b2+2ab2b+ab−62b2+a2b2+2ab2+1+1,u=−521+b2+1+a2b2+2ab2b+ab+62b2+a2b2+2ab2+1+1,v=−50−1+b2+a2b2+2ab2+1v=−−50−1+b2+a2b2+2ab2+1v=52b2+a2b2+2ab2+1+1v=−52b2+a2b2+2ab2+1+1
뒤로 대체 x=u+vix=50−50−1+b2+1+a2b2+2ab2b+ab−60−50−1+b2+a2b2+2ab2+1+−50−1+b2+a2b2+2ab2+1i,x=−50−50−1+b2+1+a2b2+2ab2b+ab+60−50−1+b2+a2b2+2ab2+1−−50−1+b2+a2b2+2ab2+1i,x=521+b2+1+a2b2+2ab2b+ab−62b2+a2b2+2ab2+1+1+52b2+a2b2+2ab2+1+1i,x=−521+b2+1+a2b2+2ab2b+ab+62b2+a2b2+2ab2+1+1−52b2+a2b2+2ab2+1+1i