Suppose that I am writing a proof or some other piece of mathematical writing, and wish to introduce $n$ distinct complex numbers, for some positive integer $n$. What are the complex numbers called?
- If $n=1$, then clearly the (unique) complex number I am interested in is called $z$.
- If $n=2$, the two complex numbers are called $z$ and $w$.
It is the case $n\ge3$ that i am concerned about. There seem to be no other standard letters for complex numbers, and all the other letters around that end of the alphabet ($x,y,u,v,t$ etc.) are reserved for real numbers. Indeed we often write $z=x+iy$ and $w=u+iv$ where $x,y,u,v$ are stipulated to be real.
What am I missing here? I can't think of any way to get around this problem. Is there a theorem in mathematics that states that every problem parametrized by $n$ complex numbers is equivalent (in some precise sense) to a problem involving just two complex numbers?
Best Answer
Subscripts! $$ z_1 = x_1 + i y_1, \dots, z_n = x_n + i y_n $$