Question

Find all the complex roots. Write the answer in the indicated form. The complex cube roots of 27(cos 234° + i sin 234°) (polar form)
A. -3(cos 78° + i sin 78°), 3(cos 198° + i sin 198°), -3(cos 318° + i sin 318°)
B. 3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), 3(cos 158° + i sin 158°)
C. -3(cos 78° + i sin 78°), 3(cos 118° + i sin 118°), -3(cos 158° + i sin 158°)
D. 3(cos 78° + i sin 78°), 3(cos198° + i sin 198°), 3(cos 318° + i sin 318°)
I know it is not A I got this one wrong

Answer 1

i think the answer is D

Answer 2

the cube root of 27 is 3
and \(243\div3=78\)

Answer 3

go around the circle again
\((234+360)\div 3=198\) and again \((234+720)\div 3=318\)

Answer 4

looks like D

Answer 5

thank you again i always second guess myself

Answer 6

when you write a number in polar form as \(r\left(\cos(\theta)+i\sin(\theta)\right)\) \(r=\sqrt{a^2+b^2}\) should be positive

Answer 7

yw