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In what ways was the introduction of imaginary numbers similar to the introduction of negative numbers and the introduction of irrational numbers to mathematics?

Answer :

The introduction of imaginary numbers similar to the introduction of negative numbers through the determination of square root of a negative number.

Imaginary numbers

Complex numbers are square root of a negative number. Since a square root of a negative number  cannot be determined, it is always represented with "i"

Given the rational number √-4 for instance, this will result in complex number or imaginary number since it is a negative number.

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