So im pretty sure i got part 1. 3 is the magnitude and its to the power of (5/6)(pi)i
Please help with the following questions cheers.
From de Moivre's formula, , the angle of one solution will be 1/n the angle of z. Note that I like to use the notation "cis theta" (pronounced "kiss theta") as shorthand for . But since cosine and sine functons have a period of , other solutions are available that are "evenly spaced" about the origin separated by the angle . In this way there are always n solutions to the nth root of z.
Let me give an example: If z = 16i, which is equal to , there are four 4th roots. The magnitude of z is 16, so the magnitude of the 4th roots are all . The angle of the first solution is at angle , and the rest are at , where k = 0, 1, 2, and 3. Thus the four 4th roots of 16i are: .
Now, can you apply this thinking to the problem at hand?