It's actually quite hard to graph complex numbers - you would need a four-dimensional space to graph them adequately. I believe it's more convenient to find zeros analytically for such functions.
For a pure imaginary number: {i = sqrt(-1)} times a real coefficient {r}, you have i*r. The cube_root(i*r) = cube_root(i)*cube_root(r), so find the cube root of r in the normal way, then we just need to find the cube root of i. For any cubic function (which has a polynomial, in which the highest term is x3) will always have 3 roots. There are 3 values, which when cubed will equal the imaginary number i:-i will do it: (-i)3 = (-i)2 * (-i) = -1 * (-i) = iThe other two are complex: sqrt(3)/2 + i/2 and -sqrt(3)/2 + i/2If you cube either of the two complex binomials by multiplying out, you will end up with 0 + i as the answer in both cases.Note: the possible roots for any cubic are: 3 real roots, or 1 real root and 2 complex root, or 1 pure imaginary root, and 2 complex roots.For your original question, if you want to stay in the pure imaginary domain, then you can use: Cube_root(i*r) = -i * cube_root(r) to find an answer.
Rational zero test cannot be used to find irrational roots as well as rational roots.
Descartes' rule of signs (see related link) can help you determine the maximum number of real roots. If the polynomial is odd powered, then there will be at least one real root. Any even powered polynomial can be factored into a bunch of quadratics [though they may not be rational or even pretty], and any odd-powered polynomial can be factored into a bunch of quadratics and one linear (this one would have the real root). So the quadratics may have pairs of real or complex roots (having an imaginary component).To clarify, when I say complex, I'm referring to the fact that there will be an imaginary component to the root, because actually the real numbers is a subset of the set of complex numbers.The order of the polynomial will tell you how many roots it will have. If you can graph the polynomial, then you can see if it crosses the x axis. If it is a 5th order polynomial, and crosses the x axis 3 times, then there are 3 real roots (the other two roots are complex).
To find the complex conjugate of a number, change the sign in front of the imaginary part. Thus, the complex conjugate of 14 + 12i is simply 14 - 12i.
The fourth square root is the 16th root of a number. On a computer, to find the 16th root of a number, say 5.6, enter 5.6^(1/16). If the number you start with is positive, you will have 2 real roots (one positive and one negative) and 14 complex roots. If it is negative, you will have 16 complex roots.
The real ones are -5 and +5.
It is +1
If you are trying do find out x it's 2. 2 to the fourth power equals sixteen.
-3/2
For school you will need to learn how to find square and cube roots in order to have the needed prerequisites to answer progressively harder and more complex problems.
4
The four roots of 4√256 are {4, -4, 4i, and -4i}. Note that two of them are real numbers and the other two are pure imaginary, therefore 0 + 4i is the same as just 4i
( +0.063246 ) and ( -0.063246 ).These numbers are rounded.These are the only square roots of 0.004. There are no more real ones,and no imaginary or complex ones.
p(x) = 0 => x4 + 2x3 + x2 + 8x - 12 = 0=> (x + 3)*(x - 1)*(x2 + 4) = 0So the imaginary roots of p(x) are the imaginary roots of x2 + 4 = 0that is x = ±2i
This quadratic equation has no real roots because its discriminant is less than zero.
1 and the positive and negative square roots of 2