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.
The fourth roots of 16(cos 200° + i sin 200°) are . Step-by-step explanation: The given expression is Using deMoivre’s Theorem The four roots are in the form of For n=1, For n=2, For n=3, Therefore the fourth roots of 16(cos 200° + i sin 200°) are .
take n=1,y=2(cos(140)+ isin (140)) take n=2,y=2(cos(230)+ isin (230)) take n=3,y=2(cos(320)+isin(320))
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