已知复数z,且(1+3i)z为纯虚数,z的模为根号10,(1)求复数Z(2)若复数W满足/2w-z/

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已知复数z,且(1+3i)z为纯虚数,z的模为根号10,(1)求复数Z(2)若复数W满足/2w-z/
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已知复数z,且(1+3i)z为纯虚数,z的模为根号10,(1)求复数Z(2)若复数W满足/2w-z/
已知复数z,且(1+3i)z为纯虚数,z的模为根号10,(1)求复数Z(2)若复数W满足/2w-z/

已知复数z,且(1+3i)z为纯虚数,z的模为根号10,(1)求复数Z(2)若复数W满足/2w-z/
(1) 假设z=a+bi
(1+3i)*z = (1+3i)*(a+bi) = a+bi+3ai-3b = a-3b + (3a+b)i 为纯虚数
因此 a-3b=0,a=3b,z=3b+bi
已知|z| = √10,得 (3b)² + b² = 10,解得 b=1
因此 z=3+i
(2) 假设w=c+di
|2w-z| = |2c+2di-3-i| = |(2c-3)+(2d-1)|