Given that z = 1/(3+it), it is denoted by T on a argand diagram
1. show that z + z* = 6zz*
Got this part out but the next part i am totally confused
I did abit of loci but i cant figure out this one
2. Show that if t varies T lies on a circle , and state the coordinates of the centre of the circle.
Please help i am clueless
Q.1
Q.2
Since we know lies on the circle, so does . Also, so will the points that are these reflected in the Imaginary axis, and .
If we join the diagonally opposite points, we get two lines that cross at the centre of the circle.
Line 1: Points and lie on the line, so
Line 2: Points and lie on the line, so
Both points have a y intercept of (0, 0), so this is clearly the point where the two lines cross. Therefore the centre of the circle is (0, 0).