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Here's how you can find any power (fractions would be a root of a number) of any number (complex or real). A real number is a subset of the complex number set, with the imaginary part = 0. I'll refer you to a related link on Euler's formula for information about how this is derived. A complex number can be graphed on the Real-Imaginary plane, with reals on the horizontal axis, and imaginary on the vertical. Convert the complex number from x-y style coordinates in this plane to polar coordinates.
For a complex number a + bi, here's how you do that. We will end up with a magnitude and an angle. The magnitude is sqrt(a² + b²). The angle is found by tan-1(b/a). Now to find a power, apply the power to the magnitude (for cube root this is exponent of 1/3). Then multiply the angle by the power (in this case you divide by 3). Really for a cube root there will be 3 distinct roots. Since a the angle of a circle is 360° or 2pi radians, you can add 2pi radians to the angle of the original complex number, then divide by 3 to determine the second root. Add 4pi radians to the original angle and then divide by 3 to determine the 3rd root. Then convert back to x-y coordinates if you want to:
Magnitude*(cos(angle) + i*sin(angle)), for each of the 3 angles that you determined.
See the question: 'Strategy for finding the cube root of complex numbers'
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How do you find the range of a radical function?
The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.
How do you cube the square root of imaginary number ex square root of 2i cubed?
From the question, it seems you already calculated the square root, or know how to get it. You can cube complex numbers just like you cube normal numbers: multiply them by themselves; the number must appear three times as a factor. For example, the cube of (2 + i) is (2+i) x (2+i) x (2+i). Another method - usually faster - to calculate any power is to express the complex number in polar form (absolute value and angle). For the specific case of a cube, the cube of such a number is the cube of the absolute value, at an angle that is three times the angle of the original number.
Finding the surface area of a cube?
Total surface area of a cube = 6*area of cube face = 6*cube side*cube side
Are triangle numbers the same as cube numbers?
No
Do negative numbers have cube roots cube roots?
Yes.
How do you find the volume of complex cube?
There is no such thing as a complex cube!
What do you think is true of the square roots of a complex number?
I posted an answer about cube roots of complex numbers. The same info can be applied to square roots. (see related links)
How do you write cubed roots?
In mathematics, a cube root of a number, denoted or x1/3, is a number a such that a3 = x. All real numbers (except zero) have exactly one real cube root and a pair ofcomplex conjugate roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8 is 2, because 23 = 8. All the cube roots of −27iareThe cube root operation is not associative or distributive with addition or subtraction.The cube root operation is associative with exponentiation and distributive with multiplication and division if considering only real numbers, but not always if considering complex numbers, for example:but
Is the cubes root of negative 125 rational?
One of them is: -5 = -5/1 The other two cube roots are complex numbers.
Why do principal cube roots of negative numbers have to be different in real numbers or complex numbers?
Probably because if you consider real numbers, you are not interested in complex numbers.Any complex number other than zero - and that includes real numbers - has three cubic roots, which have an angle of 120 degrees between one another. For example, the cubic roots of 1 are 1, 1 at an angle of 120°, and 1 at an angle of 240°. Similarly, the cubic roots of -1 are 1 at an angle of 180° (equal to -1), 1 at an angle of 60°, and 1 at an angle of 300°.
How do you find the range of a radical function?
The answer depends on what group or field the function is defined on. In the complex plane, the range is the complex plane. If the domain is all real numbers and the radical is an odd root (cube root, fifth root etc), the range is the real numbers. Otherwise, it is the complex plane. If the domain is non-negative real numbers, the range is also the real numbers.
How do you cube the square root of imaginary number ex square root of 2i cubed?
From the question, it seems you already calculated the square root, or know how to get it. You can cube complex numbers just like you cube normal numbers: multiply them by themselves; the number must appear three times as a factor. For example, the cube of (2 + i) is (2+i) x (2+i) x (2+i). Another method - usually faster - to calculate any power is to express the complex number in polar form (absolute value and angle). For the specific case of a cube, the cube of such a number is the cube of the absolute value, at an angle that is three times the angle of the original number.
Finding the surface area of a cube?
Total surface area of a cube = 6*area of cube face = 6*cube side*cube side
What are all the cube numbers up to 1000?
Those are the cubes of the numbers 1-10. Just calculate the cube of 1, the cube of 2, the cube of 3, etc., up to the cube of 10.
Finding cube using while loop in c?
int cube=1,num,i; for(i=1;i<=3;i++){ cube*=num; }
Are triangle numbers the same as cube numbers?
No
Do negative numbers have cube roots cube roots?
Yes.
