What is the Locus of Re[z^2]>1?

  • Thread starter Thread starter Grand
  • Start date Start date
  • Tags Tags
    Complex
AI Thread Summary
The locus of Re[z^2]>1 can be derived by substituting z=x+iy, leading to the inequality x^2-y^2>1. This represents the region outside the hyperbola defined by the equation x^2-y^2=1. Testing points like (0,0) and (2,0) confirms the behavior of the graph. The discussion emphasizes that understanding the graph's shape is key to solving the problem. Ultimately, the solution involves recognizing the hyperbolic nature of the inequality.
Grand
Messages
74
Reaction score
0

Homework Statement


Find the locus of Re[z^2]>1


Homework Equations





The Attempt at a Solution


Subbing in z=x+iy gives x^2-y^2>1, but where do I go from there on. It shouldn't be very tough (i.e. including analysis of functions) because the other examples in the same problem are easy.
 
Physics news on Phys.org
Well can you graph x^2-y^2=1? It should be clear where it is more than 1 either by intuition or testing some easy points such as (0,0) versus (2,0).
It is the graph of a hyperbola by the way.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

What Are the Loci for Different Values of Lambda in a Complex Equation?
Replies
14
Views
2K
Graph complex numbers to verify z^2 = (conjugate Z)^2
Replies
9
Views
3K
What Is the Modulus of z When z=(x-iy)/(x+iy)?
Replies
4
Views
2K
Find the argument of the complex number.
Replies
1
Views
1K
Least distance between two complex numbers on two loci
Replies
4
Views
3K
Geometric interpretation of complex equation
Replies
5
Views
2K
Complex Numbers: Euler's formula problem
Replies
2
Views
2K
Find the GCD of the given complex numbers (Gaussian Integers)
Replies
4
Views
2K
Complex numbers problem |z| - iz = 1-2i
Replies
20
Views
2K
Complex Number Inequality: Solving for Locus of z = (x + iy) | Homework Help
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top