What is square root of -1? Not homework. I just want to see if anyone knows?

Answer 1

Actually, -1 has two square roots, just like most numbers, but in this instance neither is a real number (in a mathematical sense). Rather, the principal root of -1 is called i. However, -1 also has a second square root, -i, and (-i)² also equals -1

If the number line is drawn on the x axis of a Cartesian coordinate plane, then i would be plotted one unit above the origin and -i would be one unit below the origin. The entire plane would then represent the set of complex numbers, with the distance to the right (or left) of the y axis being the real component and the distance above (or below) the x axis being the imaginary component. In a very real sense, complex numbers adds a whole new dimension to the real number system.

Incidentally, complex numbers are used so often in scientific and engineering calculations that computer languages intended for such calculations often have capability for handling complex numbers built into them. ANSI FORTRAN IV and the versions of FORTRAN since then have this capability. The modern versions of C, C++, and so on have libraries for representing and manipulating complex numbers. The later versions of the TI-8x graphic calculators, including the TI-86, TI-83, TI-89, and TI-84 can also perform calculations on complex numbers, including almost all of the same manipulations that can be performed on real numbers. (You still can't divide by zero though.)

Answer 2

The square of any positive or negative number is positive, and the square of 0 is 0. Therefore, no negative number can have a real square root. However, it is possible to work with a larger set of numbers, called the complex numbers, that does contain solutions to the square root of a negative number. This is done by introducing a new number, denoted by i (sometimes j, especially in the context of electricity) and called the imaginary unit, which is defined such that i2 = −1. Using this notation, we can think of i as the square root of −1, but notice that we also have (−i)2 = i2 = −1 and so (−i) is also a square root of −1.

Answer 3

The square root of 1 is 1. Square root of 0 is 0. The square root of ones head, is block, cube square.

Answer 4

the square root of -1 is: i
i ia an imaginary number defined as the square root of -1, and i squared is 1. i cubed (i^3) is -i, and i^4=1

Answer 5

its an unreal number, but used in and physics/ normally having a value of (0) or negative (1.)

Answer 6

i: imaginary number

Its not completely useless, it can be used for a lot of stuff like quantum mechanics and electromagnetism just to name a few.

Answer 7

i


i² = -1
√(-1) = i

Answer 8

While everyone has said i is the answer there is a second answer which is
- i.
:)