Solve y^3 = −1.
To solve the equation y^3 = -1, we need to find the values of y that make the equation true.
First, let's take the cube root of both sides of the equation to isolate y:
y = ∛(-1)
The cube root of -1 can be written as ∛(-1) = -1.
Therefore, the solution to the equation y^3 = -1 is y = -1.
To solve the equation, we need to find the value of y that satisfies the equation y^3 = -1.
Taking the cube root of both sides, we get:
y = (-1)^(1/3)
The cube root of -1 can be written as a complex number in trigonometric form. Let's write -1 as a complex number using Euler's formula:
-1 = e^(iπ)
Now, applying the cube root to both sides, we get:
y = e^(iπ/3)
Using Euler's formula, we can rewrite this as:
y = cos(π/3) + i sin(π/3)
Therefore, the solution to y^3 = -1 is:
y = cos(π/3) + i sin(π/3)
To solve the equation y^3 = -1, we can find the cube root of both sides of the equation. The cube root of -1 is -1, so:
y = -1