Question

Find all the cube roots of -1+3i in the form a+bi

Answer 1

First, convert it to polar coordinates. Then use the ff. formula for the roots:
\[\large(r(\cos\theta+i\sin\theta))^{1/n}=r^{1/n}\left ( \cos{\frac{x+2k\pi}{n}}+i \sin{\frac{x+2k\pi}{n}}\right )\]
where for substitute k=0, 1, 2, ... n-1
Then for each answer, convert it back to rectangular form.

Answer 2

I understand that part, but what I do not get is when I try to convert it to trig form my modulus is (radical)10 which makes my cosine a decimal.

Answer 3

\[r=\sqrt{(-1)^{2}+(3)^{2}} = \sqrt{10}\]

Answer 4

which makes my argument \[\cos \theta=-1\div \sqrt{10}\] which gives me a decimal.

Answer 5

You could use a calculator for \(\cos^{-1}{\frac{1}{\sqrt{10}}}\).

Answer 6

Thank you!

Answer 7

No problem. :D