# Help with Complex Numbers

• April 28th 2012, 07:41 AM
Molly1313
Help with Complex Numbers
Hi guys, I am new here and I would really appreciate some help. I would like to know how to solve these questions please:

Q1. (a) Vertify that the complex number z1 = 3-2i is a root of the equation z2-6z + 13=0 and find z1, the other root of this equation.

(b) On the argand diagram plot the complex numbers z1 and z2

(c) z3, is the image of z1 under the central symmetry in z2. Express z3 in the form a + bi and plot it on the argand diagram.

(d) Investigate if ¦z1-z2¦ = ¦z1¦-¦z2¦

Thank you!
• April 28th 2012, 07:46 AM
Plato
Re: Help with Complex Numbers
Quote:

Originally Posted by Molly1313

Q1. (a) Vertify that the complex number z1 = 3-2i is a root of the equation z2-6z + 13=0 and find z1, the other root of this equation.

(b) On the argand diagram plot the complex numbers z1 and z2

(c) z3, is the image of z1 under the central symmetry in z2. Express z3 in the form a + bi and plot it on the argand diagram.

(d) Investigate if ¦z1-z2¦ = ¦z1¦-¦z2¦

Just what part of this do you not understand?
See if $3+2i$ is also a root.
• April 28th 2012, 07:47 AM
Molly1313
Re: Help with Complex Numbers
The whole question unfortunately :(
• April 28th 2012, 08:10 AM
Plato
Re: Help with Complex Numbers
Quote:

Originally Posted by Molly1313
The whole question unfortunately :(

Do you understand how to evaluate $(3-2i)^2~\&~-6(3-2i)~?$
• April 28th 2012, 08:12 AM
Molly1313
Re: Help with Complex Numbers
Em, no. I feel so dumb :(
• April 28th 2012, 08:15 AM
Plato
Re: Help with Complex Numbers
Quote:

Originally Posted by Molly1313
Em, no. I feel so dumb :(

You require a live tutor. We do not provide such a service here.
• April 28th 2012, 10:02 AM
Molly1313
Re: Help with Complex Numbers
Nevermind, thanks anyway
• May 2nd 2012, 03:28 AM
PixieQ
Re: Help with Complex Numbers
Hey I have that exact question to do as well I have done part a,b and d but i can't do c can somebody help me please :)