# Math Help - complex problem

1. ## complex problem

show that the equation of the tangent to the circle mod(z)=r where r>0 at point z0 is given by ((conjugate) (z0))*z+z0*((conjugate)(z)=2*r^2

not understanding how to do this as moving point on the circumference of circle is z but what is z0

2. Originally Posted by prasum
show that the equation of the tangent to the circle mod(z)=r where r>0 at point z0 is given by ((conjugate) (z0))*z+z0*((conjugate)(z)=2*r^2

not understanding how to do this as moving point on the circumference of circle is z but what is z0

$z_0$ is a given point on the circle and $z$ is an arbitrary point on the tangent.

CB

do we have to use concept of rotation in it

4. Originally Posted by prasum
You could start by writing it in cartesians so $z=x+i y$, and $z_0=r (\cos(\theta)+i \sin(\theta))$, then plug these into the proposed equation and show that it is a straight line which passes through $z_0$ and has gradient $-1/\tan(\theta)$