Question

Q3: Solve the complex equation
s⁴ = 1/2 - √3/2i

Answer 1

To solve the complex equation s⁴ = 1/2 - √3/2i, we can convert the right side of the equation to polar form and take the fourth root of both sides. The solutions are cos(60°) + isin(60°), cos(150°) + isin(150°), cos(240°) + isin(240°), cos(330°) + isin(330°).

Step-by-step explanation:

To solve the complex equation s⁴ = 1/2 - √3/2i, we can start by converting the right side of the equation to polar form. Then, we can take the fourth root of both sides to find the value of s.

1. Write the complex number in polar form: 1/2 - √3/2i = cos(240°) + isin(240°)
2. We can now take the fourth root of both sides to find s: s = cos(60°) + isin(60°), cos(150°) + isin(150°), cos(240°) + isin(240°), cos(330°) + isin(330°)
3. Therefore, the solutions to the equation are: s = cos(60°) + isin(60°), cos(150°) + isin(150°), cos(240°) + isin(240°), cos(330°) + isin(330°)

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