已知复数z=3+bi(b∈R),且(1+3i)•z为纯虚数. (1)求复数z (2)若w= ,求复数w...
问题详情:已知复数z=3+bi(b∈R),且(1+3i)•z为纯虚数. (1)求复数z (2)若w= ,求复数w的模|w|. 【回答】.【*】(1)解:复数z=3+bi(b∈R),且(1+3i)•z为纯虚数. 即(1+3i)•(3+bi)=3﹣3b+(9+b)i为纯虚数,∴3﹣3b=0,9+b≠0,解得b=1.∴z=3+i.(2)解:w====...
问题详情:已知复数z=3+bi(b∈R),且(1+3i)•z为纯虚数. (1)求复数z (2)若w= ,求复数w的模|w|. 【回答】.【*】(1)解:复数z=3+bi(b∈R),且(1+3i)•z为纯虚数. 即(1+3i)•(3+bi)=3﹣3b+(9+b)i为纯虚数,∴3﹣3b=0,9+b≠0,解得b=1.∴z=3+i.(2)解:w====...