Complex variables- graphing an equation

sarahs52
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Homework Statement




Suppose that c is a member of the Real numbers, and p is a member of the Complex numbers with p not equal to 0, are given numbers.

(a) Show that pz + conjugate(pz) + c = 0 is the equation of a straight line in the plane.


Provide a carefully-drawn plot that illustrates your solution for a few given values of the constants c and p .


Homework Equations




z is a complex number (i.e. x+iy)


The Attempt at a Solution



a) After simplifying the conjugates: px +ipy + px - ipy + c = 0
After collecting like terms: 2px + c = 0
Solving for x: x = -0.5(c/p)


Now, I don't understand how the graph would look like. Would it be a vertical line on the real vs imaginary axes?

Thank you.
 
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Looks like it to me.
 
sarahs52 said:

Homework Statement




Suppose that c is a member of the Real numbers, and p is a member of the Complex numbers with p not equal to 0, are given numbers.

(a) Show that pz + conjugate(pz) + c = 0 is the equation of a straight line in the plane.


Provide a carefully-drawn plot that illustrates your solution for a few given values of the constants c and p .


Homework Equations




z is a complex number (i.e. x+iy)


The Attempt at a Solution



a) After simplifying the conjugates: px +ipy + px - ipy + c = 0
After collecting like terms: 2px + c = 0
Solving for x: x = -0.5(c/p)


Now, I don't understand how the graph would look like. Would it be a vertical line on the real vs imaginary axes?

Thank you.

I thought you said that p was a complex number; it does not appear so in what you have done.

RGV
 
p is a constant that is a member of the set of complex numbers. Does that make sense?
 
I see what you mean now, Ray. I think I got it now!
 
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