what is the answer of 1÷√x?
Answers
Answer:
answered the question: What is the square root of -1? Oh well. Maybe that’s what you meant?
There is no square root of -1 in the reals, because the square of every real number is nonnegative.
See Imaginary number - Wikipedia for information about imaginary numbers and complex numbers.
Rafael Bombelli simply started by declaring that something called iiwould have the property that its square is -1. If we try to add it to the real numbers, what will happen? And something wonderful happened.
If you add this ii into the real number system, and you want addition and multiplication to still work (and still have the associative law and all that), then you have to add all numbers of the form a+bia+bi where aa and bb are real numbers. Oh, when b=0b=0, you get all the real numbers back. If you multiply two of these numbers together, then you get another number of the same kind. So there is an operation of multiplication (and addition), and all the familiar laws work, like associative and commutative. This new, bigger set of numbers looks a lot like a plane full of numbers, with aa and bb playing the role of Cartesian coordinates.
The complex plane, with the complex number system, was born. It turns out these complex numbers are very useful.
Someone else added more new numbers (called jj and kk) that are also square roots of one, to get an even bigger number system called the Quaternions. Their multiplication is not commutative, and they form a four-dimensional space of numbers (unlike the 2-dimensional complex plane and 1-dimensional real line), and they turn out to be very useful too.
Combine 12 1 2 and −1 - 1 . Move the negative in front of the fraction. By the Power Rule, the integral of x−12 x - 1 2 with respect to x is 2x12 2 x 1 2 . The answer is the antiderivative of the function f(x)=1√x f ( x ) = 1 x .