Complex numbers are numbers that contain both a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part, with i representing the square root of -1.
The square root of a complex number is another complex number that, when multiplied by itself, gives the original complex number. This can be found by using the formula (a + bi)^(1/2) = ±(√a + ib√a), where a and b are the real and imaginary parts of the original complex number.
To simplify a complex number root problem, you can use the same rules as simplifying a square root. First, factor the number inside the root into its perfect square factors. Then, simplify the square root of each perfect square factor. Finally, combine any like terms and simplify if possible.
A real root is a number that, when squared, gives a real number. A complex root is a number that, when squared, gives a negative real number. In other words, a complex root has an imaginary component, while a real root does not.
Yes, a complex number root can be negative. This happens when the original complex number has a negative real part and an imaginary part. For example, the square root of -4i would be -2i since -2i * -2i = 4i^2 = -4.