An imaginary number is a special kind of number that helps us when regular numbers (called real numbers) aren't enough.
When we square a real number (multiply it by itself), we always get a positive number or zero:
• 2 × 2 = 4
• 0 × 0 = 0
• (-3) × (-3) = 9
But what if we want a number that, when squared, gives a negative answer? That doesn't happen with real numbers, so we imagine a new kind of number that makes it possible!
This new number is called the unit imaginary number and it is defined as:
i × i = -1
Its symbol is i (short for "imaginary"), or j in engineering.
Imaginary numbers are built using this idea.
Examples:
• 2i is an imaginary number that means 2 times i
• 3i is an imaginary number that means 3 times i
• and so on
So long as we keep the "i" there to remind us that we need to multiply by the unit imaginary number we are safe to proceed.