Complex numbers

arze · #1 $Old$ November 15th, 2009, 07:37 PM

Find the value(s) of z for which
$|z+2+i|=5$ and $Re(z-1)=0$

Attempt:
$|z+2+i|=5$ is a circle with center (-2,-1) radius 5.
My problem is with $Re(z-1)=0$ , i don't know how to resolve it.
Thanks

Chris L T521 · #2 $Old$ November 15th, 2009, 07:45 PM

Quote:

Originally Posted by arze $View Post$

Find the value(s) of z for which
$|z+2+i|=5$ and $Re(z-1)=0$

Attempt:
$|z+2+i|=5$ is a circle with center (-2,-1) radius 5.
My problem is with $Re(z-1)=0$ , i don't know how to resolve it.
Thanks

Take $z=x+iy$ . So $\text{Re}\left(z-1\right)=0\implies \text{Re}\left(x-1+iy\right)=0\implies x-1=0\implies x=1$ .

With this, we see that $z=1+iy$ .

To find the imaginary part, substitute z into the equation for the circle.

Can you take it from here?