Complex numbers -2

[curicuri]

I have a problem of exact the same kind. Should I perhaps make a new post for this or could we continue with this problem here?

Problem
Determine z that satisfies the following condition:
Im(z)y≤Re(z)+1


Solution
If z=x+yi --> y≤x+1.
The line Im(z)=Re(z)+1 is included.


My question.
I am actually quite lost here. I actually do not see at all what numbers to use to make this triangle?

 

[ksdhart2]

The only thing I can figure is that you've made a small typo in your exercise and it's supposed to be simply \(Im(z) \le Re(z) + 1\) with no extraneous \(y\) on the left-hand side of the inequality.

With that correction made, the textbook's given solution pretty much spells out all of the steps. The most convenient way to plot a complex number on an x-y coordinate grid is to let the x-axis represent the real numbers and the y-axis represent the imaginary numbers. In this way, we define a generic complex number as \(z = x + yi\). For example, the number \(w = 3 + 4i\) would be plotted on the x-y grid at the point (3, 4). From that definition, it follows that \(Im(z) = y\) and \(Re(z) = x\), and if you make these substitutions you're left with the inequality \(y \le x + 1\). Try graphing that inequality and see what you get.

 

[pka]

I have a problem of exact the same kind. Should I perhaps make a new post for this or could we continue with this problem here?
Problem
Determine z that satisfies the following condition: \(\displaystyle Im(z)≤Re(z)+1\)
My question.
I am actually quite lost here. I actually do not see at all what numbers to use to make this triangle?

Note that there is really no triangle in the solution. The actual solution is a half-plane union its edge.
My question to you is: "can you tell us what set of points satisfy \(\displaystyle x-3y\le 6\)? That is simple precalculus question.

 

[curicuri]

Great input understand it now