Square root of a negative number
Date: Wed, 23 Nov 1994 12:58:34 -0800 From: (Paul Pragin) Is it theoretically possible to calculate the square root of a negative number?
Date: Mon, 28 Nov 1994 16:51:23 -0500 (EST) From: Dr. Sydney Subject: Re: your mail Hi there! Thanks for writing to Dr. Math. Taking the square root of a negative number is a problem that mathematicians struggled with for a very long time. It was not until the 1600's and 1700's that the great mathe- maticians really got a firm grasp on what the square root of a negative number is. Why were there so many problems? From the basic axioms that describe the real numbers we see that a positive real times a positive real yields a positive real and a negative real times a negative real yields a negative real. So, in the real numbers it is impossible to square a number and get a negative number. So, a new field had to be introduced: the complex field. Do you know what complex numbers are? The square root of -1 was given the name i (i is for imaginary). All numbers that are square roots of negative numbers can be written as a real number times i. Do you see how this works? How would you write the square root of -5 in terms of i? I hope this helps answer your question. If you have any more questions, please do write back. --Sydney, a math doctor
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