若复数z满足于(1+2i)=3+4i的绝对值(i为虚数单位),求z

问题描述:

若复数z满足于(1+2i)=3+4i的绝对值(i为虚数单位),求z

设z=a+bi
(1+2i)z
=(1+2i)(a+bi)
=a+bi+2ai-2b
=3+4i;
所以
a-2b=3;
2a+b=4;
a=11/5;
b=-2/5;
z=11/5-2i/5
Z的模=√(121+4)/25=√5;