Question

Помогите! ПОЖАЛУЙСТА.Найти корень 3 степени из -64i

Answer 1

512 я думаю) но не уверен

Answer 2

4^3 степени будет 64.

Answer 3

Finding the Cube Root of -64i

To find the cube root of -64i, we can use the following steps:

1. Express -64i in Polar Form: - To find the polar form of -64i, we can use the formula \(r = \sqrt{a^2 + b^2}\) and \(\theta = \arctan\left(\frac{b}{a}\right)\), where \(a\) and \(b\) are the real and imaginary parts of the complex number, respectively.

2. Apply the Cube Root Formula in Polar Form: - Once we have the polar form of -64i, we can apply the cube root formula in polar form, which states that the cube roots of a complex number in polar form \(r(\cos\theta + i\sin\theta)\) are given by \(\sqrtr}(\cos\frac{\theta + 2k\pi}{3} + i\sin\frac{\theta + 2k\pi}{3})\), where \(k = 0, 1, 2\).

3. Calculate the Cube Roots: - Using the formula for the cube roots in polar form, we can calculate the three cube roots of -64i.

Let's proceed with these steps to find the cube root of -64i.