Find the fourth roots of 16(cos 200° + i sin 200°).

See below.

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.

Root #1:

Part 3: Solving for root #2

To solve for root #2, follow the same simplifying steps above but change k  to k = 1.

Root #2:

Part 4: Solving for root #3

To solve for root #3, follow the same simplifying steps above but change k to k = 2.

Root #3:

Part 4: Solving for root #4

To solve for root #4, follow the same simplifying steps above but change k to k = 3.

Root #4:

The fourth roots of 16(cos 200° + i(sin 200°) are listed above.

c. 4 and 1/2 pounds is the answer! : )

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation: