Question

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

Answer 1

Answer:

$z_m=-\frac{1}{2}-\frac{1}{2}i$

Step-by-step 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,

$z_m=\frac{a_1+a_2}{2}+\frac{a_1+a_2}{2}i$.

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;

$z_m=\frac{z_1+z_2}{2}$

$\Rightarrow z_m=\frac{-8+3i+7-4i}{2}$

$\Rightarrow z_m=\frac{-8+7+3i-4i}{2}$

$\Rightarrow z_m=\frac{-1-i}{2}$

$\Rightarrow z_m=-\frac{1}{2}-\frac{i}{2}$

or

$\Rightarrow z_m=-\frac{1}{2}-\frac{1}{2}i$