The discussion revolves around finding the center and radius of a circle defined by a complex number equation involving loci. Participants are tasked with sketching the loci and determining the geometric properties of the circle.
Some participants have provided guidance on expressing the complex ratio in a different form, while others have questioned the initial calculations of the radius. There is a mix of interpretations regarding the correct approach to finding the center and radius, with some participants expressing uncertainty about the methods being discussed.
There is mention of homework constraints and the need to adhere to specific mathematical theorems related to circles and complex numbers. Some participants express confusion about the transformations required to analyze the complex equation.
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.