已知复数Z1=a+i,Z2=1+bi(a,b∈R),i为虚数单位. (Ⅰ)若a=1,b=2,求Z2Z1; (Ⅱ)若Z1+Z2为纯虚数,Z1-Z2为实数,求a,b.

问题描述:

已知复数Z1=a+i,Z2=1+bi(a,b∈R),i为虚数单位.
(Ⅰ)若a=1,b=2,求

Z2
Z1

(Ⅱ)若Z1+Z2为纯虚数,Z1-Z2为实数,求a,b.

(Ⅰ)∵a=1,b=2,∴Z1=1+i,Z2=1+2i,∴Z2Z1=1+2i1+i=(1+2i)(1−i)(1+i)(1−i)=3+i2;(Ⅱ)∵Z1+Z2=a+i+1+bi=(a+1)+(b+1)i为纯虚数,∴a+1=0b+1≠0①;又Z1-Z2=(a-1)+(1-b)i为实数,∴1-b=0②,由①②得...