Question

复数题,Z1是虚数,z2=z1+(1/z1)是实数,且z1大于等于-1,小于等于1

Answer 1

设z1=a+bi,z2=a+bi+1/a+bi=a+bi+(a-bi)/a^2-b^2

b-b/a^2-b^2=0 a^2-b^2=1

z1的模=根号（a^2-b^2）=1