Mathematics: Given z = 3 − 4i and = −1 + 5i: a. find the distance betwen z and b. find the midpoint of the segment joining z and

Given z = 3 − 4i and = −1 + 5i: a. find the distance

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07.01.2022

a) 9.22 units

b) 2+0.5i

Step-by-step 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

$s=\sqrt{2^2+(-9)^2}\\\Rightarrow s=9.22\ units$

Distance between them is 9.22 units

b) Midpoint

$\frac{3+1}{2}+\frac{-4i+5i}{2}\\ = 2+0.5i$

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

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