来自陈立潮的问题
若复数Z满足Z^2=-2,则Z^3等于?
若复数Z满足Z^2=-2,则Z^3等于?
1回答
2020-03-1006:57
若复数Z满足Z^2=-2,则Z^3等于?
若复数Z满足Z^2=-2,则Z^3等于?
令Z=a+bi
(a+bi)^2=a^2-b^2+2abi=-2
a^2-b^2=-2
2ab=0
a=0,b=2^1/2orb=-2^1/2
Z=+-2^(1/2)i
Z^3=2*2^(1`/2)i
orZ^3=-2*2^(1/2)i
2^(1/2)表示根号2