There's no such thing as the square root of a negative number. Right?
Since squaring a number is defined as multiplying it by itself, and multiplying a negative times a negative gives a positive, all squares should be positive. Right?
So any number you want to take the square root of should be positive to begin with. Right?
So what if it's not?
What do you do...
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Do you use a different version of FOIL?
Do you just multiply 8x4x(-9)?
or do you multiply 8iX4i which equals 32 but then mutliply it by -1 because i^2=-1 so you'd have -32, and then multiply...

Complex Numbers
In algebra, there are two types of numbers: real numbers and imaginary numbers. Real numbers refer to any ordinary number (e.g. 1, 2, 3 . . .) while imaginary numbers are . . . well . . .
imaginary! They don't really exist, they are represented by a real number with the letter
i next to it. For example, 3i is an imaginary number.
Complex numbers are those consisting...
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I was very fortunate to have been taking electronics at the same time I was learning high school trigonometry. Like most folks, I was never good at abstract math, but being able to see physical demonstrations of math principles was a huge help.
One of the real "bears" for most math students is the concept of the imaginary number...and yet it's crucial to working with all alternating...
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