Question

Find the midpoint between the complex numbers. Show all work for full credit. z1= -8 + 3i z2= 7 - 4i

Answer 1

`z_m=-(1)/(2)-(1)/(2)i`

Explanation:

The given complex numbers are;

`z_1=-8+3i`

and

`z_2=7-4i`.

The midpoint of any two complex numbers,

`z_1=a_1+a_1i` and
`z_2=a_2+a_2i` is

is given by,

`z_m=(a_1+a_2)/(2)+(a_1+a_2)/(2)i`.

The midpoint of the complex numbers can be found by adding the corresponding real parts and imaginary parts and then dividing each by 2.

This is the same as;

`z_m=(z_1+z_2)/(2)`

`\Rightarrow z_m=(-8+3i+7-4i)/(2)`

`\Rightarrow z_m=(-8+7+3i-4i)/(2)`

`\Rightarrow z_m=(-1-i)/(2)`

`\Rightarrow z_m=-(1)/(2)-(i)/(2)`

or

`\Rightarrow z_m=-(1)/(2)-(1)/(2)i`