Math Help - Complex Number: Indicate Graphically

1. Complex Number: Indicate Graphically

I don't understand question c and d. Is c really just asking |x| <= 3? In the back of the book it says the answer for (c) "vertical strip consisting of all (x, y) such that -3<= x <= 3, -∞ <= y <= ∞.
For (d) I'm completely lost. Can anyone help me with these two?

NOTE: This is actually from Coddington's ODE's book. I didn't know if I should post this in the Precalculus or Differential Equations section.

2. Re: Complex Number: Indicate Graphically

Hey ILovePizza.

You are correct that if z = x + iy then |Re(z)| <= 3 is the same as |x| < 3.

Hint: For d remember that Im(z) = y if z = x + iy.

Remember that if you no restrictions on the other variable then you must include all values for that other variable.

3. Re: Complex Number: Indicate Graphically

I am puzzled as to why you would even consider that. Surely you know that "Re(z)" is not anything like "|z|". If, for example, z= 1+ 10000i, $|z|= \sqrt{1000^2+ 1}= \sqrt{1000001}$, far larger than "3" while |Re(z)|= 1< 3.

If z= x+ iy then |Re(z)|= |x|< 3. Where is that on an xy- coordinate system?

4. Re: Complex Number: Indicate Graphically

I guess what I'm really asking is...

Why is it that the answer says: vertical strip consisting of all (x, y) such that -3 ≤ x ≤ 3, -∞ ≤ y ≤ ∞? Are the x and y supposed to be (Re z, Im y)? Because for some reason when I enter this in mathematica

And yet part of the answer is answered for -3 ≤ x ≤ 3. But the other part says -∞ ≤ y ≤ ∞ <---- Where is that coming from? Are those supposed to be Imaginary numbers? And where is the vertical strip? o_o

5. Re: Complex Number: Indicate Graphically

Originally Posted by ILovePizza
I guess what I'm really asking is...

Why is it that the answer says: vertical strip consisting of all (x, y) such that -3 ≤ x ≤ 3, -∞ ≤ y ≤ ∞? Are the x and y supposed to be (Re z, Im y)? Because for some reason when I enter this in mathematica
And yet part of the answer is answered for -3 ≤ x ≤ 3. But the other part says -∞ ≤ y ≤ ∞ <---- Where is that coming from? Are those supposed to be Imaginary numbers? And where is the vertical strip? o_o
The program is graphing $|x|\le 3$. That is not the graph in the complex plane.

$\{z:|\text{Re}(z)|\le 3\}=\{(x+yi):|x|\le 3\}$ is the set in the complex plane.
That set can be represented as a set of ordered pairs in the $xy\text{-plane}~:\{(x,y):-3\le x\le 3\}$.
That is a vertical strip $xy\text{-plane}$.