Chapter 9.6B, Problem 7GCE

To determine

To find the location of the complex number z that satisfy the given equation in complex plane.

Explanation of Solution

Given:

The given complex number is $\left|z-(1-i)\right|=5$

Calculation:

Consider the complex number-

  $\begin{array}{l}\left|z-(1-i)\right|=5\\ \left|(x+iy)-(1-i)\right|=5\\ \left|x-1+i(y+1)i\right|=5\\ $ {(x-1)}^2+{(y+1)}^2=5$\end{array}$

The graph of the above equation is-

All these points lie on the circumference of circle given as

  $(-1,0),(0,1),(0,-3),(3,0)$