Chapter 6, Problem 100CR

To determine

To calculate:

The distance between the following complex number:

  $1+5i,-1+3i$

Answer to Problem 100CR

The distance between the given complex number is $\sqrt{5}units$

Explanation of Solution

Given information:

  $1+5i,-1+3i$

Formula used:

The distance between the two complex numbers is given by the following expression:

  $d=\sqrt{{\left(s-a\right)}^2+{\left(t-b\right)}^2}$

Calculation:

Know that:

  $\begin{array}{l}a+bi=1+5i\\ s+ti=-1+3i\end{array}$

Now, the distance between the given complex numbers is calculated as:

  $d=\sqrt{{\left(s-a\right)}^2+{\left(t-b\right)}^2}$

Put the given data:

  $\begin{array}{l}d=\sqrt{{\left(-1-1\right)}^2+{\left(3-5\right)}^2}\\ d=\sqrt{{\left(-2\right)}^2+{\left(-1\right)}^2}\\ d=\sqrt{5}units\end{array}$