It is known that the corresponding points of complex numbers Z1 and Z2 in the complex plane are a (- 2,1), B (a, 3) respectively (1) If the absolute value of z1-z2 = root 5, find the value of A (2) The complex z = z1z2, the corresponding point is on the bisector of two or four quadrants, and the value of a is obtained

It is known that the corresponding points of complex numbers Z1 and Z2 in the complex plane are a (- 2,1), B (a, 3) respectively (1) If the absolute value of z1-z2 = root 5, find the value of A (2) The complex z = z1z2, the corresponding point is on the bisector of two or four quadrants, and the value of a is obtained

The corresponding points of complex numbers Z1 and Z2 in the complex plane are a (- 2,1), B (a, 3)
Z1=-2+i
Z2=a+3i
Z1-Z2=(-2-a)-2i
|Z1-Z2|
=√[(2+a)²+4]
=√5
∴(2+a)²=1
2 + a = 1 or - 1
A = 1 or - 3
（2）
Complex z = z1z2 = (- 2 + I) (a + 3I) = - (2a + 3) + (a-6) I
The corresponding point is on the bisector of two or four quadrants
∴(2a+3)=(a-6)
a=-9

If Z1 = 2 - I, Z2 = 1 + 3I, then the imaginary part of complex I / Z1 + Z2 / 5 is

i/z1=i(2+i)/(2-i)(2+i)=(-1+2i)/(4+1)=-1/5+2/5i
z2/5=1/5+3/5i
i/z1+z2/5=1/5+2/5i+1/5+3/5i=2/5+i
The imaginary part is 1I

Given the imaginary number Z satisfies | 2Z + 5 | = | Z + 10 | to find | Z|

Let z = x + Yi (x, y ∈ R, and Y ≠ 0), then
（2x+5）^2+(2y)^2=(x+10)^2+y^2.
We get x ^ 2 + y ^ 2 = 25
∴|z|=5