复数3+4i的平方根怎么算?
设 a,b∈R (a+bi)²=3+4i a²-b²+2abi =3+4i ==> a²-b² =3 .....(1) 2ab=4.............(2) (2) ==>a =2/b -->(1) ===>4/b² -b² =3 ===>b=1 ,a=2 或b=-1, a=2 ===>复数3+4i的平方根 2+i 或-2-i
答:1)设z的平方根是x+yi,则 (x+yi)^2=3+4i --->(x^2-y^2)+2xyi=3+4i由复数相等的条件:x^2-y^2=3,2xy=4 解方...详情>>
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