Question

Given z = 3 − 4i and ???????? = −1 + 5i:

a. Find the distance betwen z and ????????.
b. Find the midpoint of the segment joining z and ????????.

Answer 1

a) 9.22 units

b) 2+0.5i

Explanation:

`z_1=3-4i`

`z_2=-1+5i`

`z_1-z_2=(3-4i)-(1+5i)\\\Rightarrow z_1-z_2=3-4i-1-5i\\\Rightarrow z_1-z_2=2-9i`

a) Distance between them is

`s=√(2^2+(-9)^2)\\\Rightarrow s=9.22\ units`

Distance between them is 9.22 units

b) Midpoint

`(3+1)/(2)+(-4i+5i)/(2)\\ = 2+0.5i`

The midpoint of the egment joining
`z_1` and
`z_2` is 2+0.5i