- #1
Amaru58
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Homework Statement
Find the cartesian equation of the locus |z+3+2i|=Re(z)
Homework Equations
The Attempt at a Solution
You let z= x +iy
therefore Re(z)=x?
Indeed. So you now haveAmaru58 said:Homework Statement
Find the cartesian equation of the locus |z+3+2i|=Re(z)
Homework Equations
The Attempt at a Solution
You let z= x +iy
therefore Re(z)=x?
You're there. The canonical form in Cartesian coordinates is usually f(x,y) = 0 or f(x,y) = const., which is what you have there.Amaru58 said:OK. I'm not too sure what you mean by canonical form?
Would x = {(x+3)^2 + (y+2)^2}^1/2
Therefore: x^2 = x^2 +6x + 9 +y^2 +4y+4
6x+4y+y^2=-13
I'm not quite sure what to do now
Thanks for the help
A complex number locus is a set of points on a complex plane that satisfy a specific condition or equation. It is similar to a graph in the real number system, but instead of plotting points on a horizontal and vertical axis, complex numbers are plotted on a horizontal and vertical axis representing the real and imaginary parts respectively.
To graph a complex number locus, you first need to determine the equation or condition that the points must satisfy. Then, plot the points on a complex plane and connect them to form a shape. You can also use technology, such as a graphing calculator, to help you graph the locus.
Some common examples of complex number loci include circles, ellipses, and hyperbolas. These shapes can be described by equations involving complex numbers, such as z = a + bi, where a and b are real numbers and i is the imaginary unit.
Complex number loci have many real-life applications, particularly in science and engineering. They are used to model and analyze electrical circuits, fluid flow, and other physical systems. They also have applications in computer graphics, cryptography, and signal processing.
The complex number locus question is significant because it helps us understand the behavior and properties of complex numbers. By studying and graphing complex number loci, we can gain insights into the relationships between real and imaginary numbers and how they interact with each other. This knowledge is essential in many fields of mathematics and science.