Complex variables- graphing an equation

[sarahs52]

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.

 

[kru_]

Looks like it to me.

 

[Ray Vickson]

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

 

[sarahs52]

p is a constant that is a member of the set of complex numbers. Does that make sense?

 

[sarahs52]

I see what you mean now, Ray. I think I got it now!