Question

|(z)-(z/3)|=1
find the range to which |z| belongs

Answer 1

z is complex? If so z=x+iy

\[|x+iy-\frac{x+iy}{3}|=1\]

Answer 2

\[|\frac{2x+2iy}{3}|=1\]
\[\frac{2x+2iy}{3}\] Is just some other complex number with real part\[\frac{2}{3}\] and imaginary part also\[\frac{2}{3}\]

Answer 3

Where w is that complex number. Find the modulus by pythagoras, and you have an equation with a, b and constants.

Answer 4

\[|w|=\sqrt{(\frac{2x}{3})^2+(\frac{2y}{3})^2}=1\]