Chapter 6, Problem 101CR

To determine

To calculate:

The midpoint of the line joining by the following complex number:

  $1+i,4+3i$

Answer to Problem 101CR

The midpoint of the line joining by the given two complex numbers is $C=\left(\frac{5}{2},2\right)$ .

Explanation of Solution

Given information:

  $1+i,4+3i$

Formula used:

The midpoint of the line joining by the complex numbers is given by the following expression:

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

Calculation:

Know that:

  $\begin{array}{l}a+bi=1+i\\ s+ti=4+3i\end{array}$

The midpoint of the line joining by the given two complex numbers is calculated as:

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

Put the given data:

  $\begin{array}{l}C=\left(\frac{1+4}{2},\frac{1+3}{2}\right)\\ C=\left(\frac{5}{2},\frac{4}{2}\right)\\ C=\left(\frac{5}{2},2\right)\end{array}$