Chapter 6, Problem 23CT

To determine

To calculate:

Midpoint of the segment joining the points.

Answer to Problem 23CT

The midpoint of line segment the points $z_1=5i$ and $z_2=-6+i$ is $-3+3i$

Explanation of Solution

Given information:

  $z_1=5i$ and $z_2=-6+i$

Calculation:

When comparing $z_1=5i$ with $a+bi$ ,

  $a=0,b=5$

Similarly, $z_2=-6+i$ with $s+ti$

  $s=-6,t=1$

By using mid-point of line segment,

  $=\frac{a+s}{2}+\left(\frac{b+t}{2}\right)i$

Put the values,

  $\begin{array}{l}=\left(\frac{0+\left(-6\right)}{2}\right)+\left(\frac{5+1}{2}\right)i\\ =-3+3i\end{array}$

The midpoint of line segment the points $z_1=5i$ and $z_2=-6+i$ is $-3+3i$ shown as below,