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Most famously, an imaginary number, that is, a number whose square (which is the number multiplied by itself) is negative. All real numbers have positive squares. A complex number, is a number which is the sum of a real number and an imaginary number, and so is also a non-real number.
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Is -4 a nonreal complex number?
No. Negative four is a real number. All real numbers are also complex numbers, so it is a complex number (but it's real, not nonreal)
How many solutions are in x2 plus x plus 4 equals 0?
There are none. For this equation, there is nonreal answer, as the graph of the quadratic does not pass below the x-axis
What are solutions that are not real in algebra?
An example would be a negative number found from using the quadratic formula. That can possibly result from an equation that cannot be set into factored form due to the lack of common factors. Imaginary numbers can be considered nonreal. 2i = 2 times radical -1 The radical looks like the pulse monitor you see in hospitals, fyi.
3x2 - 7x plus 6 equals 0?
Nonreal answer if we put it into the quadratic equation 0=ax^2bx+c x=(-b[+/-](b^2-4ac)^0.5)/2a x=(7[+/-](7^2-4*3*6)^0.5)/(2*3) x=(7[+/-](49-72)^0.5)/6 x=(7[+/-]((-23)^0.5))/6 x=(7[+/-]((-23)^0.5)/6 As you cannot have the square root of a negative number (unless to take iinto account, but lets not go there) the quadratic does not cross the x-axis, so there a no real values that can be found to solve the equation (which i assume you are trying to do).
What are nonreal numbers?
The square of 0 is 0. For any other number, whether it is positive or negative, the square is positive. Thus, the square of any real number is non-negative. This means that only non-negative number can have square roots.So what happens if you are trying to solve the equation x^2 +4 = 0. It is not a particularly complicated equation.Simplify to x^2 = -4 and so x = sqrt(-4). But then what? 2*2 = 4 and (-2)*(-2) is also 4 so neither can be an answer.To get around that, mathematicians introduced imaginary numbers. Then, the answer to the above question is that x = 2i (2j if you are a physicist). And they added the special rule for multiplication: i*i = -1. These are the simplest form of non-real numbers.The next level up are complex numbers and these are numbers of the form a + bi where a and b are real and i is the imaginary number representing the square root of -1.Yet another level up are the quaternions which are numbers of the form a + bi + cj + dk where a, b, c and d are real, and i,j k are similar to the i of the complex numbers but with further multiplication rules for i, j and k. See the link below for more on quaternions.http://en.wikipedia.org/wiki/Quaternion
