Answer:
<em>See below.</em>
Step-by-step explanation:
To find roots of an equation, we use this formula:
where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).
In this case, n = 4.
Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.
Part 2: Solving for root #1
To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by and simplify.
<u>Root #1:</u>
Part 3: Solving for root #2
To solve for root #2, follow the same simplifying steps above but change <em>k</em> to k = 1.
<u>Root #2:</u>
Part 4: Solving for root #3
To solve for root #3, follow the same simplifying steps above but change <em>k</em> to k = 2.
<u>Root #3</u>:
Part 4: Solving for root #4
To solve for root #4, follow the same simplifying steps above but change <em>k</em> to k = 3.
<u>Root #4</u>:
The fourth roots of <em>16(cos 200° + i(sin 200°) </em>are listed above.