ELI5: Explain Like I'm 5

Function of several complex variables

Okay kiddo, let me explain the function of several complex variables in very simple terms.

A function is like a magic machine that takes a number as an input and gives you another number as an output.

Imagine you have a toy car and there are many buttons on top. Each button does something different, like one button makes the car go forward, one button makes it turn left, and so on.

Now imagine instead of buttons, there are many numbers that you can put into the toy car. And instead of just one number coming out, there are actually many numbers that come out depending on the combination of numbers you put in. That's what a function of several complex variables is like.

But what's a complex number you may ask? Well, we usually use real numbers like 1, 2 or 3 in everyday life. Those are numbers that you can count with your fingers. But complex numbers are different because they have two parts: a real part and an imaginary part.

It's like you have a sandwich and you can choose what filling you want (real number), but you also get to choose what sauce you want (imaginary number). So a complex number is like a yummy sandwich with two different things inside.

A function of several complex variables is like putting your sandwich into the toy car and seeing what comes out. It's a bit like when you mix different colors of paint together - you get a new color that's different from the ones you started with.

Scientists and mathematicians use functions of several complex variables to study a lot of things, like how heat moves through different materials or how electricity flows through circuits.

So now you know that a function of several complex variables is like a magic machine that takes in complex numbers and gives out other complex numbers, and it helps smart people study lots of cool things.