Please help complex numbers

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

Re: Please help complex numbers

Quote:

Originally Posted by

**righteous818** 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

Are you using z* to represent the conjugate of z?

Re: Please help complex numbers

Re: Please help complex numbers

Quote:

Originally Posted by

**righteous818** 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).

Re: Please help complex numbers

shouldn it be reflected on the real axis

Re: Please help complex numbers

Quote:

Originally Posted by

**righteous818** shouldn it be reflected on the real axis

No, conjugates are already reflected in the real axis.

Re: Please help complex numbers

strange this is from an examination board an they gave the anser in their markscheme as the centre (1/6 , 0)

Re: Please help complex numbers

but how can you assume that the points reflected on the imaginary axis is on the circle , arent if u are doin that then you already assume that the centre is (0,0)