Question

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

Answer 1

Please, you have to apply the De Moivre formula, I write your number as below:
\[16*[\cos(200+k*360)+i*son(200+k*360)]\]
then, your roots are:
\[2[\cos(50+k*45)+i*\sin(50+k*45)]\]
where k=0, 1, 2, 3
Please substitute those values for k and you will get all of your roots.

Answer 2

Sorry not k*45 but, k*90, namely th correct ormula is:
\[2[\cos(50+k*90)+i*\sin(50+k*90)], k=0, 1,2 ,3\]

Answer 3

for example if we set k=0, we have the first root, namely:
\[2[\cos50+i*\sin50]\]
please do the same with k=1, 2, 3