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What is the relationship between the degree and the number of roots counting multiplicities?
In the complex field, the two numbers are the same. If you restrict yourself to real solutions, the relationship is as follows: A polynomial of degree p has p-2k real solutions where k is an integer such that p-2k is non-negative. [There will be 2k pairs of complex conjugate roots.]
What is the complex conjugate of 8?
Oh, isn't that just a happy little question? The complex conjugate of a real number like 8 is just 8 itself because there is no imaginary part to change. Just like how every tree needs its roots, every real number needs its complex conjugate to stay balanced and harmonious. Just remember, there are no mistakes, only happy little accidents in math!
What is the cube root of 2?
There are 3 cube roots and these are:the real root -1.2599and the complex roots 0.6300 - 1.0911i and its conjugate, 0.6300 + 1.0911i.
Which arithmetic operation requires the use of complex conjugate?
It can be used as a convenient shortcut to calculate the absolute value of the square of a complex number. Just multiply the number by its complex conjugate.I believe it has other uses as well.
What is the equation for whose roots are 4i -3i and 3i?
The equation is:x3 - 4x2i - 9xi2+ 36i3 = 0Note: The ' i ' must be an ordinary constant, and can't be sqrt(-1).If it were sqrt(-1), then -4i would also be a root of the equation.Imaginary or complex roots always occur in conjugate pairs.If -4i is also a root of the equation and the questioner just forgot to include it,then ' i ' can be sqrt(-1), and the equation can bex4 + 25x2 + 144 = 0
