Square Root of Negative 1


The square root of negative 1 is the number, which multiplied by itself, is -1. In other words, the square of this number equals minus one. If you have been looking for square root of negative one then you are right here, too. On this page you can also find what its parts are called, and in addition to the terminology of √-1 we also have a calculator you don't want to miss. Read on to learn everything about the sqrt -1.

\sqrt{-1}= \pm i

Extracting the root is the inverse operation of ^2:

\sqrt[2]{-1}\times \sqrt[2]{-1}= i^{2}\sqrt[2]{-1}^{2} = -1\sqrt[2]{1} = -1\hspace{3px}x\hspace{3px}1 = -1 = i^{2}

The term can be written as

\sqrt{-1} \hspace{3 mm}o\hspace{3 mm} \sqrt[2]{-1}

Like any negative number, -1 has two square roots: \sqrt[2]{-1} = i, which is called principal square root, and −\sqrt[2]{-1} = -i. Together, they are denominated as ± \sqrt[2]{-1}\hspace{3 mm}and are complex numbers.

Although the principal square root of negative 1 is only one of the two square roots, the term "square root of negative 1" usually refers to the principal root.

If you want to know how to find the square root of negative 1 then read the section article Square Root of Negative Number on our home page.

What is the Square Root of -1

You already know the answer to what is the square root of negative 1 and about the inverse operation of -1 square root. Keep reading to learn what the parts of it are called.

\sqrt[n]{a}= b
n = index, 2 is the index.
a = radicand, the radicand is the number below the radical sign, -1 is the radicand here.
b = root = ±i
√ is called radical symbol or radical only.
\sqrt[2]{-1}= \pm i

Now you really know all about square root of negative 1, including its parts and the inverse. If you like to learn the square root of any non-negative real number use our calculator below: Insert the number of which you like to find the square root (e.g. 1), then press the calculate button.

Number:
Square Root:±

Bookmark this calculator now!

Besides the square root of negative 1, frequently searched square roots on this site include:

Square Root of Negative One

If you have been searching for whats the square root of -1 or square root -1 the you have come to the right site, too.

The same is true if you typed sq root of -1 or -1 root in the search engine of your preference, just to name a few similar terms.

To sum up,

\sqrt{-1}= \pm i

The negative square root of -1 is -i, and the positive sqrt -1 is i. Make sure to understand that √-1 and -1 squared, -1 x -1 = 1, are not the same.

Finding the square root of negative 1 is the inverse operation of squaring the √-1. In other words (±i)2 = -1.

Further information can be found on our page square root. Note that you can also find frequents roots including √-1 by using the search form in the sidebar of this website.

If our article about sqrt -1 has been useful to you, then please give us a like or press all social buttons. If you have any question about square roots of -1 then use the comment form below.

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