No.
(-i)2
= (-1 x i)2
= (-1)2 x i2
= 1 x i2
= i2
= -1
but if it is written
-i2
Then
= -i2
= (-1) * i2
= -1 * -1
= 1
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.
the square is positive always.Except in the case of an Imaginary number. An imaginary number is a number that gives a negative result when squared,where i= √-1
Ordinarily, the square root of -70 does not exist since a positive number squared or a negative number squared results in a positive number. If complex numbers are permitted, then the square root of -70 is i√70 ~= 8.367i where i is the imaginary square root of -1 such that i2 = -1.
By definition, i^2=-1 Which also means: i=sqrt(-1) This may seem odd that such a number can be, since you may notice that all normal numbers, when squared, result in a positive number (e.g. (-3)^2=9, 0^2=0, 2^2=4). These "normal" numbers are called real numbers. Numbers that result in a negative number when squared are called "imaginary numbers". They don't lie on the real number line. i is the imaginary unit, just like 1 is the real unit. Don't let the names confuse you, imaginary numbers can be just as real and useful as real numbers, that's just a name that stuck with them.
When a negative number is squared, the negative sign is essentially squared along with the number, resulting in a positive value. However, when taking the square root of a positive number, we are looking for the value that, when squared, gives us the original positive number. Since both a positive and negative number can square to the same positive value, the convention is to consider the principal (positive) square root by default. The negative square root is also a valid solution in many contexts, but for simplicity and consistency, the positive square root is typically chosen.
The basic theory of imaginary numbers is that because (-) numbers squared are the same as (+) numbers squared there is not a correct continueos line on a graph.
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.
yes they do
the square is positive always.Except in the case of an Imaginary number. An imaginary number is a number that gives a negative result when squared,where i= √-1
Any real number, when squared will give a positive real number. This is true weather you have a negative real number and square it, or positive. The concept of imaginary numbers was invented to handle equations which needed to use the square root of a negative number, in order to solve them.At first, they were not considered useful beyond this, so they were named imaginary numbers. Through the work of Euler and others, it became evident that imaginary and complex numbers could be useful, especially when analyzing waves, such as electrical waveforms.
An imaginary number is a number, which when squared, gives a negative real number. Any positive or negative real number, when squared, will give a positive real number. Imaginary numbers were originally conceived (around the 1500's) to provide solutions to equations which required there be a solution to the square root of a negative real number. Originally, that was the only purpose that they served, so they were given the term imaginary. The imaginary numbers were shown to be graphically at a 90° angle to real numbers. Complex numbers are the combination of real and imaginary numbers, and can be plotted graphically on a complex plane, just like you would plot x and y coordinates on a regular 2-dimensional plane.Through the work of Euler in the 1700's and others, a relationship between imaginary numbers and the behavior of waves and oscillating motion was worked out. See related link for some interesting information about imaginary and complex numbers.
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.
Ordinarily, the square root of -70 does not exist since a positive number squared or a negative number squared results in a positive number. If complex numbers are permitted, then the square root of -70 is i√70 ~= 8.367i where i is the imaginary square root of -1 such that i2 = -1.
(-1)2=1 all squared numbers turn out positive and 12=1 (-1)2=1 all squared numbers turn out positive and 12=1
no,a negative number cannot have a square root .it is made only for positive numbers .but,yes,negative numbers can be squared.
This is an interesting question. Looking at complex numbers graphically, zero is at the intersection of the real and imaginary axis, so it is 0 + 0i. But if you square zero, you get zero, which is not a negative number (a pure imaginary, when squared will give a real negative number), so I'd have to say it is not imaginary.
By definition, i^2=-1 Which also means: i=sqrt(-1) This may seem odd that such a number can be, since you may notice that all normal numbers, when squared, result in a positive number (e.g. (-3)^2=9, 0^2=0, 2^2=4). These "normal" numbers are called real numbers. Numbers that result in a negative number when squared are called "imaginary numbers". They don't lie on the real number line. i is the imaginary unit, just like 1 is the real unit. Don't let the names confuse you, imaginary numbers can be just as real and useful as real numbers, that's just a name that stuck with them.