Question

I'm using De Moivre's theorem to get all the solutions for z^4 =i but I'm unsure how to get the angle theta. Do I use r or the polar form?

Answer 1

is that supposed to be z^4 = 1? or i?

Answer 2

SEE \[\phi = \tan^{-1} y/x\]

Answer 3

Z^4 = i
If z = x +iy

so x is zero and y is 1

Answer 4

\[e ^{i \theta} \]You can work it now ..

Answer 5

\[y/x \rightarrow \infty\]\[\theta = 90\]

Answer 6

hmmm....i really think it should be:
\[x^{4} = 1\]
The fourth roots of unity.
If you use wolfram with the equation:
\[x^{4} = i\]
you get some pretty bizarre answers.
and yeah,
\[e^{i\theta}\]
is used with the nth roots of unity, where:
\[\theta = \frac{2\pi}{n}\]
so in this case, since n = 4
\[\theta = \frac{2\pi}{4} = \frac{\pi}{2}\]
That would be the angle hes looking for.

Answer 7

same answers lol, now we know its right.

Answer 8

Thanks