What is an imaginary number?

Updated: 4/27/2022
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9y ago

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The square root of a negative real number is an imaginary number.

We know square root is defined only for positive numbers.

For example,

1) Find the square root of (-1)

It is imaginary. We say that square root of (-1) is i.

In fact they are not real numbers.

2) Find the square root of (-4)

-4 can be written as (-1)(4)

Square root of 4 is 2 and square root of (-1) is i

So, the square root of -4 is 2i.

Similarly, we can find the square root of other negative numbers also.

An imaginary number is defined to handle square roots of negative numbers. The imaginary unit i is defined as the 'positive' square root of -1.

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Q: What is an imaginary number?
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Can a number be imaginary but not pure imaginary?

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Can a no real number be a pure imaginary number?

If a number is pure imaginary then it has no real component. If it is a real number, then there is no imaginary component. If it has both real and imaginary components, then it is a complex number.

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An imaginary number is a number that has the square root of -1 as one of its factors.

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