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z = y i where y is a real number

1: z^(1/3) = y^(1/3) (cos(30 deg) + i sin(30 deg))

2: z^(1/3) = y^(1/3) (-sin(60 deg) + i cos(60 deg))

3: z^(1/3) = y^(1/3) (- i)

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Q: What are the cube roots of an imaginary number in trigonometric form?
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Related questions

What are the 3 cube roots of -1?

4


How many real cube roots does any positive number have?

there is no cube roots in negative


What can be determined from roots of real numbers?

The short answer is "Nothing". In the complex domain, the number of nth roots of any real number is n. Every non-negative real number has 2 square roots. Every real number has 3 cube roots. Every non-negative real number has 2 real square roots and 2 imaginary ones. and so on. So what?


How do you find cube roots of imaginary numbers?

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.


What is prime with cube roots?

All numbers have cube roots (not necessarily integral cube roots) so every prime has cube roots.


Do negative numbers have cube roots cube roots?

Yes.


How many cubed roots are there in number 27?

There are 3 cube roots of 27. There are 2 square roots of 27 ( or any real number ). There are 4 fourth roots of 27 and so on:)


How do you determine the cube root of 7?

Many calculators will offer a way for you to do cube roots, or what number to the power of 3 will equal that number. There is no easy way to go about finding cube roots without a calculator, so I suggest not trying too hard.. but the cube root of 7 is 1.912931182772389 found from using a simple Cube Root calculator you can find on the internet.


What is a number that has more than two square roots?

There is no number that has more than two square roots.By definition, the "square" bit implies two.Every number has exactly:TWO square roots,THREE cube roots,FOUR quadratic roots,etc.


What is the significance of cube and cube roots?

you are my friend


What are the cube numbers between 50 and 70?

Every number between 50 and 70 is a cube. For example, 53 is the cube of the cube root of 53 = 3.7563 (approx).The perfect cube roots in the range is 64.


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)