Complex numbers are divided into real and imaginary parts, such as complex number z=a+bi, a.

It's called the real part, B.

This is called imaginary part, I.

It is called imaginary unit, and I 2 =-1. The addition rule of complex numbers is that the real part is added to the real part and the imaginary part is added to the imaginary part. Pure imaginary number refers to a complex number with only imaginary part, that is, a=0 and b≠0. So this question says that z is a pure imaginary number, which means that its real part is zero. So z should be converted into +bi form. This involves the simplification of (a+2i)/( 1+i): multiply (1-i) up and down, and then (a+2i)/(1+i) = (a+2i) (1-i). So the complex number z = (a+2)/2+(2-a) i/2+(3-i) = [(a+2)/2+3]+[-ai/2], and then let the real part [(a+2)/2+3]=0 to get a.

Extension: a≠0, b=0, called real number.

This is familiar to the landlord.

A=0, b≠0 is called pure imaginary number.

Just talk

A=0 and b=0, which means 0.

A≠0, b≠o, is a universal plural.