Find the indicated roots. Write the answer in trigonometric form.
-Fifth roots of 243(cos 280° + i sin 280°)
A) 3(cos 280° + i sin 280°), 3(cos 370° + i sin 370°), 3(cos 460° + i sin 460°), 3(cos 550° + i sin 550°),3(cos 595° + i sin 595°)
B) 3(cos 56° + i sin 56°), 3(cos 146° + i sin 146°), 3(cos 236° + i sin 236°), 3(cos 326° + i sin 326°),3(cos 371° + i sin 371°)
C) 3(cos 280° + i sin 280°), 3(cos 352° + i sin 352°), 3(cos 424° + i sin 424°), 3(cos 496° + i sin 496°),3(cos 568° + i sin 568°)
D) 3(cos 56° + i sin 56°), 3(cos 128° + i sin 128°), 3(cos 200° + i sin 200°), 3(cos 272° + i sin 272°),3(cos 344° + i sin 344°)

Question

Quizplus · Accepted Answer

The fifth roots of a complex number in trigonometric form are found by dividing the angle by 5 and adding multiples of 360°/5 to find all roots. Here, 280°/5 = 56°, and the roots are 56° apart: 56°, 128°, 200°, 272°, and 344°.

Find the Indicated Roots