How do I sketch the locus of |z - 5-3i | = 3 on an Argand Diagram?

First, we use the idea that a complex number z can be written in terms of its real and imaginary parts, i.e. z = x+iy, to write our expression as:

 

| x+ iy -5 - 3i | = 3

Next, we can group the real and imaginary parts of the above expression, giving us:

| (x-5) + i(y -3) | = 3

 

Now that the expression is in the form a+ib, we can use that the modulus of a complex number is the square root of (a2 + b2), to write our expression as:

[ (x-5)2 + (y-3)]1/2 = 3

 

Finally, by squaring both sides of the equation, we get:

 

(x-5)2 + (y-3) = 32

 

This sort of expression should look familiar to you; it's the standard equation for a circle!  So our final plot on our Argand diagram is of a circle center (5,3) with a radius of 3. By extending the ideas we've considered in this example, it follows that the expression |z- z1| = r represents a circle centered at z1 = x1 + iy1, with a radius r

GM
Answered by Gyen ming A. Further Mathematics tutor

26043 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the set of values for which: 3/(x+3) >(x-4)/x


Use de Moivre’s theorem to show that, (sin(x))^5 = A sin(5x) + Bsin(3x) + Csin(x), where A , B and C are constants to be found.


What's the best way to solve projectile problems in Mechanics?


Let A, B and C be nxn matrices such that A=BC-CB. Show that the trace of A (denoted Tr(A)) is 0, where the trace of an nxn matrix is defined as the sum of the entries along the leading diagonal.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences