If a number is pure imaginary then it has no real component. If it is a real number, then there is no imaginary component. If it has both real and imaginary components, then it is a complex number.
if there is no integer answer, they are irrationalex. sq root 5 is irrational but sq root 9 = 3 so it is rational,integer, counting numberif you are taking sq root of a negative they are imaginary ex. sqroot (-9)=========================The square roots of all positive real numbers are real numbers.The square roots of all negative real numbers are imaginary numbers.Some square roots are rational, but the vast majority are irrational.
A complex number is any number that is in the real/imaginary plane; this includes pure reals and pure imaginaries. The difference between two numbers inside this plane is never outside this plane; therefore, yes, the difference between two complex numbers is always a complex number. However, the difference between two numbers that are neither purely imaginary nor purely real is not always necessarily a number that is neither purely imaginary nor purely real. Take x+yi and z+yi for instance, where x, y, and z are all real: (x+yi)-(z+yi)=x+yi-z-yi=x-z. Since x and z are both real numbers, x-z is a real number.
There is no specific term for such polynomials. They may be referred to as are polynomials with only purely complex roots.
Yes, the only argument would be the example, i + (-i) = 0. However, many people don't realize that 0 is both a purely real and pure imaginary number since it lies on both axes of the complex plane.
No. It's purely imaginary.
real roots= Overdamped equal roots= critically damped complex roots /imaginary roots = Underdamped
An imaginary number is a square root of a negative number. Imaginary numbers have the form bi where b is a non-zero (real number) and i is the imaginary unit, defined as the square root of − 1.if we define 'imaginary numbers' as 'complex numbers having a real part as 'zero' and a non-zero imaginary part'.. 0 doesn't fit in this description. But by, convention and for theoretical symmetry , we'll have to define 'real numbers' in pretty much the same way, and hence 0 would neither be a purely imaginary number or a purely real number.Overall i would say that 0 is a real number. Imaginary numbers only involve square roots of negative numbers.http://wiki.answers.com/Is_the_zero_imaginary_number#ixzz16w9viQWx
No.Suppose bi and di are two complex purely imaginary numbers such that b and d are real.Thenbi * di = bdi2 = -bd which is real.
A complex number has a real part and a (purely) imaginary part, So imaginary numbers are a subset of complex numbers. But the converse is not true. A real number is also a member of the complex domain but it is not an imaginary number.
No real roots. Imaginary roots as this function does not intersect the X axis.
The square roots of any positive real number are a positive and a negative real number. The square roots of any negative real number are a positive and a negative imaginary number. The square roots of any imaginary number or any complex number are two complex numbers.
There are no real numbers, only in the imaginary field they are -6i and 6i where i is the imaginary square root of -1.
In the context of algebra, the term real root refers to the solution to an equation which consists of a real number rather than an imaginary or complex number (a complex number being a combination of real and imaginary numbers). You may recall that any given equation will have the same number of roots (or solutions) as the highest exponent in the equation, so that if you are dealing with x squared, you have two roots. Often there would be one real root and one imaginary root. In general, the real roots are more useful, although there are some circumstances in which imaginary or complex roots are also relevant to what you are doingl.
Square roots of negative numbers are complex, meaning that they carry a 'real' and an 'imaginary' part. Here the real part is approximately 5.8309518948453 and the imaginary part is i.
The eigen values of a real symmetric matrix are all real.