Consider this puzzle: What is the square root of –1? We know that . We also know that . There is no Real Number that, when multiplied by itself, results in a negative number. Thus, cannot exist on number line.

Question

KnowledgeBoat · Accepted Answer

It is true that cannot exist on the real number line. Reason : By Brahmagupta's laws : ⇒ A positive number multiplied by a positive number gives a positive number : (+) × (+) = (+). ⇒ A negative number multiplied by a negative number gives a positive number : (-) × (-) = (+). So, the square of any real number (positive, negative or zero) is always non-negative. There is no real number whose square is -1. Hence, has no place on the real number line. To handle expressions like , mathematicians invented a new kind of number called the Imaginary Unit, denoted by i, where : ⇒ i2 = -1 ⇒ i = . This led to the development of Imaginary Numbers, which extend the real number line into a new dimension and form the basis of Complex Numbers (numbers of the form a + bi, where a and b are real numbers). Imaginary numbers are essential in modern electrical engineering, quantum mechanics, signal processing and several other fields. Hence, does not exist on the real number line; it is denoted by i, the imaginary unit, which forms the foundation of complex numbers.

Mathematics

Consider this puzzle: What is the square root of –1? We know that . We also know that . There is no Real Number that, when multiplied by itself, results in a negative number. Thus, cannot exist on number line.

Whole Numbers

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