In algebra, imaginary numbers are part of the complex number system in which real numbers cannot measure.
The symbol for imaginary numbers is i. You can define what i is equivalent to, but you cannot measure it in real terms.
i is equal to the square root of -1.
This means that i2 is equal to -1.
Therefore, i3 is equal to -i, or the negative square root of -1.
Hence, i4 is equal to 1.
This pattern of i, -1, -i, and 1 continues ad infinitum in the same exact manner shown.
Simplyfing In Terms of i[edit | edit source]
With i, you can simplify the square roots of negative numbers.
Defining Complex Numbers[edit | edit source]
All complex numbers have a real part and an imaginary part. This can be shown as follows:
, where a is real and b is imaginary.
Below are several examples of complex numbers.
, and even are all complex numbers.
Multiplying Complex Numbers[edit | edit source]
Multiplying complex numbers is not that much different than multiplying algebraic expressions. I'll show you how so below.
1. Copy the problem...
2. LOIF it (Last - Outside - Inside - First), which is like FOIL in reverse...
3. Combine like terms...
WATCH OUT! You're not done! Remember, i2 = -1.
4. Simplify the exponents...
5. And combine the like terms again for the final answer.