- #1
dfollett76
- 19
- 0
Does i, the imaginary number, have a square root? This was bothering me for a while, then I thought I happened upon a simple solution, but have since forgetten.
[tex]\sqrt{i}=?[/tex]
[tex]\sqrt{i}=?[/tex]
whozum said:From Orion1:
[tex] w_1 = \text{cis} \; 225^{\circ} = ( \cos 225^{\circ} + i \sin 225^{\circ}) [/tex]
Is the cis() function equivalent to cos() + i sin()
?
abia ubong said:i don't know if my answer is of any relevance since i am always ignored or insulted.
but i did a work of mine and got +or-[i/rt2] *[1-i].you can tell me if i am wrong
noslen said:keep it simple-
i^(1/2) = (-1)^(1/4)
The square root of i is a complex number that, when squared, equals i. In other words, the square root of i is any number that, when multiplied by itself, gives you i.
The value of the square root of i depends on the context in which it is used. In general, the two possible values for the square root of i are 1/sqrt(2) + i/sqrt(2) and -1/sqrt(2) - i/sqrt(2).
To find the square root of i, you can use the complex number form of the square root theorem. This states that the square root of a complex number can be found by taking the square root of its magnitude and dividing its argument by 2.
The square root of i is a specific type of imaginary number, as it is a complex number with a real part of 0 and an imaginary part of 1. It is often used in mathematics and physics to solve equations involving imaginary numbers.
The square root of i is important in mathematics and science because it allows for the simplification of complex equations involving imaginary numbers. It also has applications in quantum mechanics and electrical engineering.