What Does I Squared Equal

What are imaginary numbers?

For starters: despite the given name, imaginary numbers are NOT imaginary. They exist, and tin be useful in some cases.

Unremarkably, when we employ our calculators to try and notice the negative square root of a number, nosotros receive this error message:

=

Although, thanks to imaginary numbers, we don't have to come across this error message anymore. There is a way to detect the square root of a negative number, and that mode is called 'i' (the unit of measurement for imaginary numbers).

Imaginary numbers tin can be written as real numbers multiplied by the unit i (imaginary number). For example, the foursquare root of a negative number could be an imaginary number.

The square root of -16 = 4i (4 times the imaginary number)

An imaginary number could as well be divers equally the negative outcome of any number squared.

iv^2 = -16

Considering ordinarily, iv^ii would equal +xvi, but because we are using the unit i, (4)(4) = -16i. We could too use this method for negative squares. For example, (-iv)(-4) = -16i.

When using imaginary numbers, nosotros can await past these mathematical laws:

(+)(+) = (+)
(-)(-) = (+)
(+)(-) = (-)
(-)(+) = (-)

And nosotros tin make these equations possible:

(+)(+) = (-)
(-)(-) = (-)
(+)(-) = (+)
(-)(+) = (+)

[source]

"Algebra" (Novel):

"Algebra" is a book written by Italian mathematician Rafael Bombelli. In this book, he had explained the rules for multiplying existent numbers with positives and negatives. Here is how he explained information technology:

"Plus times plus makes plus
Minus times minus makes plus
Plus times minus makes minus
Minus times plus makes minus
Plus viii times plus 8 makes plus 64
Minus five times minus 6 makes plus 30
Minus 4 times plus 5 makes minus 20
Plus 5 times minus 4 makes minus 20"

He also explained the laws of multiplying circuitous numbers:

"Plus past plus of minus, makes plus of minus.
Minus by plus of minus, makes minus of minus.
Plus by minus of minus, makes minus of minus.
Minus past minus of minus, makes plus of minus.
Plus of minus by plus of minus, makes minus.
Plus of minus by minus of minus, makes plus.
Minus of minus past plus of minus, makes plus.
Minus of minus by minus of minus makes minus."

[source] (Notation: These laws were direct copied from Wikipedia equally the original text was taken direct from the book "Algebra.")