The two square roots of i are (k, k) and (-k, -k) where k = sqrt(2)/2 = 1/sqrt(2).
The square roots of any positive real number are a positive and a negative real number. The square roots of any negative real number are a positive and a negative imaginary number. The square roots of any imaginary number or any complex number are two complex numbers.
No, but it is irrational, because there is no rational number whose square is two. Imaginary numbers are the square roots of negative numbers.
Square roots of negative numbers are imaginary.
In mathematics, there is a distinction between real numbers and imaginary numbers. There is a number known as i which means, the square root of minus one. Since any number that we know of will produce a positive result when multiplied by itself, there would seem to be no such thing as the square root of minus one, however, the concept is useful for certain purposes, nonetheless, and it is therefore known as an imaginary number. Any multiple of i is also an imaginary number (such as 67i and so forth). So, some square roots are real numbers, and some are imaginary. Both types can be called square roots.
This depends on whether you include imaginary numbers. The imaginary unit i is defined such that i² = -1. So the square root of -1 will be either i or -i. So the answer is there are 2 square roots for any number. Now if you are at a level of mathematics, which does not yet consider i, then the answer is you cannot take the square root of a negative.
The square roots of any positive real number are a positive and a negative real number. The square roots of any negative real number are a positive and a negative imaginary number. The square roots of any imaginary number or any complex number are two complex numbers.
No, but it is irrational, because there is no rational number whose square is two. Imaginary numbers are the square roots of negative numbers.
Square roots of negative numbers are imaginary.
Yes, if the number whose square root we are taking is greater than 0. Only if you try to take the square root of a negative number will you get back an imaginary number. Square roots are often irrational, but that's different from real versus imaginary.
In mathematics, there is a distinction between real numbers and imaginary numbers. There is a number known as i which means, the square root of minus one. Since any number that we know of will produce a positive result when multiplied by itself, there would seem to be no such thing as the square root of minus one, however, the concept is useful for certain purposes, nonetheless, and it is therefore known as an imaginary number. Any multiple of i is also an imaginary number (such as 67i and so forth). So, some square roots are real numbers, and some are imaginary. Both types can be called square roots.
There are none. Negative numbers don't have square roots. Well, they do, but they are known as imaginary numbers, and there is no way to determine them. A square root of a number is a number you can multiply by itself and get the original number. There is no number you can multiply by itself to get a negative number, but every positive number has two square roots of the same absolute value.
The numbers 1 and negative 1 (-1) are both square roots of positive 1.The square root of negative 1 is the "imaginary" number i.
This depends on whether you include imaginary numbers. The imaginary unit i is defined such that i² = -1. So the square root of -1 will be either i or -i. So the answer is there are 2 square roots for any number. Now if you are at a level of mathematics, which does not yet consider i, then the answer is you cannot take the square root of a negative.
There are no real numbers, only in the imaginary field they are -6i and 6i where i is the imaginary square root of -1.
None, it involves the square root of a negative number so the roots are imaginary.
Imaginary and complex numbers are an extension of the Real Number system. They are not called unreal. An imaginary number is a non-existent number, like the square root of a negative number. For example, the square root of -4 is 2i (i stands for imaginary). There are also complex numbers, which are defined as the sum of a real number and an imaginary number (e.g. 4 + 3i). An imaginary number does not exist, but can nevertheless be useful in certain applications. An imaginary number is any number that is the product of a real number and the square root of negative one (-1). The square root of -1 is the "unit" of the set of imaginary numbers, and is referred to as "i". As you know, negative numbers cannot have square roots, and so the square root of any negative number is "imaginary". There are also "complex numbers", which are the sum of a real number and an imaginary number. For example 3 + 2i.
A positive real number, such as 17, has two square roots. One is the one your calculator gives you, if you use the square root function. The other is the same number, with a minus sign in front. None of these has an imaginary part. There are no additional complex roots that have a non-zero imaginary part.