Kajan thana said:Homework Statement
Sketch the loci, find centre point and the radius of the circle.
args((z-3i)/((z+4))=π/6[/B]
Homework Equations
args(x/y)=args(x)-args(y)
Circle theorem - inclined angle theoremThe Attempt at a Solution
I sketched the circle with major arc.
Radius= using Pythagorus I got the radius as 5 unit^2 .
H=O/sinθ . H=2.5/sin(π/6)
I am stuck on finding the centre point.
[/B]
I don't know how to change it into that form.Ray Vickson said:Your radius is wrong.
Write ##z = x + iy## and express the ratio ##(z-3i)/(z+4)## as ##A(x,y) + i B(x,y)##. How can you get the equation of the curve in terms of the functions ##A(x,y)## and ##B(x,y)##?
The coordinates are (0,3) and (-4,0)mfb said:Can you find one or two points on the circle?
With a complex z and c:$$\frac c z = \frac{cz^*}{zz^*}$$Kajan thana said:I don't know how to change it into that form.
I finally got the answer right and the radius is 5 unit^2. Your way gave me the same answer as well.mfb said:With a complex z and c:$$\frac c z = \frac{cz^*}{zz^*}$$
Here * is the complex conjugation. Now the denominator is real and you can split the fraction into real and imaginary part.
Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e. the square root of -1). They are important in mathematics because they allow us to solve equations that cannot be solved with real numbers alone, and they have many practical applications in fields such as engineering and physics.
To graph a complex number on the complex plane, plot the real part of the complex number on the x-axis and the imaginary part on the y-axis. The point where these two values intersect is the location of the complex number on the complex plane.
A locus is the set of all points that satisfy a given condition or equation. In the context of complex numbers, a locus can be represented as a geometric shape on the complex plane. For example, the locus of points with a fixed distance from a given complex number is a circle on the complex plane.
To find the equation of an arc on the complex plane, you first need to determine the center point and radius of the arc. Then, you can use the equation (x-c)^2 + (y-d)^2 = r^2, where (c,d) is the center point and r is the radius, to represent the arc on the complex plane.
The principal branch of a complex logarithm is the branch that gives the "principal" or main value of the logarithm. It is defined as the logarithm of a complex number that has a positive real part and an argument in the interval (-π,π]. This branch is often used in calculations involving complex numbers.