Q: Why is an imaginary number squared equal to a a negative number?

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If I understand the question correctly, the answer is not in real numbers. But in the complex domain, there is the imaginary number i is such that i2 = -1. And so, for any positive x, [i*sqrt(x)]2 = i2*x = -1*x = -x, which is negative.

Because the square root of -25 would be that number that, squared, would equal -25. No number, positive or negative, can result in a negative square. Since -25 is a negative number, no number, positive or negative, can be squared to equal -25.

Because it's not. However, if you were to take the square root of -16, the answer would be 4i, which is an imaginary number, considered imaginary because multiplication of a real number by itself cannot equal a negative number.

No - a square root of a negative number is an imaginary number. for example, sqrt(-9) is equal to 3i.

It's equal to positive b squared, or (b x b) .

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If I understand the question correctly, the answer is not in real numbers. But in the complex domain, there is the imaginary number i is such that i2 = -1. And so, for any positive x, [i*sqrt(x)]2 = i2*x = -1*x = -x, which is negative.

No. Negative three squared is POSITIVE nine. The square of ANY number is positive, because if you multiply a negative number by a negative number, the result is positive.

Either 2i or -2i, when squared equal -4.

Because the square root of -25 would be that number that, squared, would equal -25. No number, positive or negative, can result in a negative square. Since -25 is a negative number, no number, positive or negative, can be squared to equal -25.

A negative number squared equals a positive number. When multiplying, odd numbers of negatives result in a negative answer, and even numbers of negatives result in a positive answer.

No, it equals positive 9. Any negative number squared will always give a positive result; the square root of a negative number is always imaginary (a mathematical term, referring to 'i'). So, (-3)2 = 9 and -32 = -9.

The mathematical importance of an imaginary number is to allow the result of a square root of the imaginary number to equal a negative number. One can find more extensive information on imaginary numbers and their importance on the Wikipedia website.

Because it's not. However, if you were to take the square root of -16, the answer would be 4i, which is an imaginary number, considered imaginary because multiplication of a real number by itself cannot equal a negative number.

The symbol "i" is an imaginary number used in algebra, equal to the square root of negative one.

If I ask Answers™ "what is pi squared?" I find "It is approximately equal to 3.14 but in reality pi is an imaginary number that has no end." The answer also goes on to tell me that imaginary numbers cannot be multiplied by themselves. Now i must see what y'all have to say about imaginary numbers...

Pi is the mathematical formula for the circumference of a circle. It is approximately equal to 3.14 but in reality pi is a number that has no end. Pi is NOT an imaginary number. (Imaginary numbers are the square roots of negative numbers. Whoever previously wrote this entry is an overconfident idiot who wouldn't even be able to pass Algebra II).To square any number, you multiply that number by itself.So, approximately:Pi squared is 9.869604401Pies are usually circular but there is no reason why they cannot be made in square-shaped (not sqair!).

No - a square root of a negative number is an imaginary number. for example, sqrt(-9) is equal to 3i.