# Why is the square root of negative one an imaginary number?

## Why is the square root of negative one an imaginary number?

Here, the term “imaginary” is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero (which has one double square root).

**Is the square root of a negative number imaginary?**

If the value in the radicand is negative, the root is said to be an imaginary number. The imaginary number i is defined as the square root of negative 1.

### Can imaginary roots be negative?

Imaginary roots appear in a quadratic equation when the discriminant of the quadratic equation — the part under the square root sign (b2 – 4ac) — is negative. If this value is negative, you can’t actually take the square root, and the answers are not real. Observe that when s=0, you simply have the real numbers.

**What is the square of a negative imaginary number?**

The square root don’t exist for the negative number. Therefore it’s said imaginary. It can be written as square root of (-1) multiplied by the square root of (x). And square root of (-1) is i or j commonly known as iota.

#### What is the square root of negative 2 imaginary number?

There is no real number multiplied by itself that will equal -2. Note: since negative times negative equals positive, one could therefore conclude that -1.414 i is also a correct answer to the square root of negative 2.

**How do you know if roots are imaginary?**

To determine the nature of roots of quadratic equations (in the form ax^2 + bx +c=0) , we need to caclulate the discriminant, which is b^2 – 4 a c. When discriminant is greater than zero, the roots are unequal and real. When discriminant is equal to zero, the roots are equal and real.

## Can zeros be imaginary?

State the possible number of positive real zeros, negative real zeros, and imaginary zeros of h(x) = –3×6 + 4×4 + 2×2 – 6. Since h(x) has degree 6, it has six zeros. However, some of them may be imaginary. Thus, the function h(x) has either 2 or 0 positive real zeros and either 2 or 0 negative real zeros.

**What is the square root of a negative imaginary number?**

It as simple as of the square root of positive number. The square root don’t exist for the negative number. Therefore it’s said imaginary. It can be written as square root of (-1) multiplied by the square root of (x). And square root of (-1) is i or j commonly known as iota. And it represents imaginary number.

### Which is the square root of minus one?

The principal square root of minus one is i. It has another square root −i. I really dislike the expression ” the square root of minus one”. Like all non-zero numbers, −1 has two square roots, which we call i and −i. If x is a Real number then x2 ≥ 0, so we need to look beyond the Real numbers to find a square root of −1.

**Is the square root of −1 a real number?**

Like all non-zero numbers, −1 has two square roots, which we call i and −i. If x is a Real number then x2 ≥ 0, so we need to look beyond the Real numbers to find a square root of −1. Complex numbers can be thought of as an extension of Real numbers from a line to a plane. The unit in the x direction is the number 1.

#### Is the square root of 9 positive or negative?

“Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3)2 = (+3)2 = 9.