Asked by majorbill
The system of equations:
|z-2-2i|=sqrt(23),
|z-8-5i|=sqrt(38)
has two solutions z_1 and z_2 in complex numbers. Find (z_1+z_2)/2.
My first instinct on this problem was to square each equation given that the square of the magnitude of a complex number is much easier to deal with than its magnitude alone.
I hoped to be able to then substitute in for z, but I quickly ran into problems given that the magnitude squared is the complex number times the conjugate of that number.
I don't know how to express these magnitudes squares' in terms of z and the conjugate. Any help is much appreciated :)
|z-2-2i|=sqrt(23),
|z-8-5i|=sqrt(38)
has two solutions z_1 and z_2 in complex numbers. Find (z_1+z_2)/2.
My first instinct on this problem was to square each equation given that the square of the magnitude of a complex number is much easier to deal with than its magnitude alone.
I hoped to be able to then substitute in for z, but I quickly ran into problems given that the magnitude squared is the complex number times the conjugate of that number.
I don't know how to express these magnitudes squares' in terms of z and the conjugate. Any help is much appreciated :)