Evaluate cuberoot of z given that z =8(cos264degrees + isin264degrees)
To evaluate the cube root of z, we can use the formula for finding the cube root of a complex number in polar form.
Given that z = 8(cos(264 degrees) + isin(264 degrees)), we can convert this to polar form by using the following relations:
- cos(theta) = Re^(i*theta)
- sin(theta) = Ie^(i*theta)
In this case, r = 8 and theta = 264 degrees.
So z can be expressed as z = 8e^(i*264 degrees).
Now, to find the cube root of z, we need to take the cube root of the magnitude (r) and divide the argument (theta) by 3.
The magnitude of the cube root of z is the cube root of 8, which is 2.
The argument of the cube root of z is 264 degrees divided by 3, which is 88 degrees.
Therefore, the cube root of z can be written as:
cube root of z = 2(cos(88 degrees) + isin(88 degrees))