square root of -1

Meaning

1. 1nounsingularmathematics

   The imaginary unit, written i, which is the number whose square equals negative one.

   Grammar: Used with the: the square root of -1 is written i, and in engineering it is often written j.

   Patterns

   • the square root of -1 is i

   Mathematicians introduced i as the square root of -1 so that every quadratic equation would have a solution.

   No real number can equal the square root of -1, because squaring any real number gives a positive result or zero.

   In electrical engineering, the square root of -1 is usually written j to avoid confusion with current.

Common combinations

define the square root of -1

Euler helped popularize the way we define the square root of -1.

the square root of -1 is i

Remember that the square root of -1 is i, so i squared equals -1.

multiples of the square root of -1

Pure imaginary numbers are multiples of the square root of -1.

complex numbers built on the square root of -1

Complex numbers are built on the square root of -1 and a real part.

Synonyms and how they differ

imaginary unit

Imaginary unit is the formal name for the same quantity, and it does not describe how the number is defined.

i

The letter i is the shorthand symbol, used in equations, while the longer phrase explains the idea in words.

j

The letter j is the same number in engineering notation, chosen to avoid clashing with the symbol for current.

Word family

imaginary number noun

a number that is a real multiple of i

complex number noun

a number with a real part and an imaginary part

square root noun

a number that gives another when multiplied by itself

imaginary adjective

in mathematics, involving the square root of a negative number

Commonly confused: square root of -1 or square of -1?

Practice

Make it your own

Write a sentence using “square root of -1”, then check it and compare it with the examples above.

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