1已知x,y是共轭复数,且（x-y)^2+xyi=26+4i,求|x|2设复数z满足1-z/1+z=i,求|1+z|3已知实数x满足(1-3i)x^2+ax=3-i(a∈R),求a的值题多了点,期待大家的回答,

Question

1已知x,y是共轭复数,且（x-y)^2 +xyi = 26+4i ,求|x|
2设复数z满足1-z/1+z=i,求|1+z|
3已知实数x满足(1-3i)x^2+ax=3-i (a∈R),求a的值
题多了点,期待大家的回答,

Answer 1

这种复数的题目主要是把实部和虚部分开
1.设x=a+bi,y=a-bi
（x-y)^2 +xyi = -4b^2 +(a^2+b^2)i= 26+4i
联立-4b^2=26和(a^2+b^2)=4
2.这个题目应该是设复数z满足1-1/z+z=i,求|1+z| 吧
设z=a+bi,
1-(a-bi)/[(a+bi)(a-bi)]+z=1-(a-bi)/(a^2+b^2)+a+bi
分开实部和虚部=1-a/(a^2+b^2)+a+bi/(a^2+b^2)+bi=i
则联立1-a/(a^2+b^2)+a=0和b/(a^2+b^2)+b=1
3.(1-3i)x^2+ax=3-i
联立x^2+ax=3和-3i*x^2=-i