Question

How to square imaginary numbers

Answer 1

1.Take the principle square root of a negative number.
2 Write a complex number in standard form.
3.Add and subtract complex numbers.
4.Multiply complex numbers.
5. Divide complex numbers.

Answer 2

 Imaginary numbers are numbers that can be written as a real number times i.

So what is a real number, and what is i?

Well, the real numbers are all the positive numbers, negative numbers, and zero. These are numbers like

  5 
 -2.9
 -4/3 
  0
  1.11211211111221312211131122211113213211... 
   (bonus points if you can tell us 
   what the next few digits are and why!)

So the real numbers are the numbers that you probably already know: they're the ones on the number line.

What is i? It's the square root of -1 (see footnote below). And it's NOT a real number.  i was invented because people wanted to be able to take square roots of negative numbers, and you can't do that if you limit yourself to real numbers.

So we can make an imaginary number by taking a real number like 5 and multiplying it by i. That gives us 5i. Some other imaginary numbers are

 37.3i 
  1.11211211111221312211131122211113213211i 
 Pi*i.

Note that the square of any imaginary number (except 0) is a negative number.

Complex numbers are numbers like 7 + .4i; they're a real number plus an imaginary number.

Footnote: actually, there are TWO numbers that are the square root of -1, and those numbers are i and -i , just as there are two numbers that are the square root of 4, 2 and -2.