Question

Find the solution to the following equation (using the complex number theory):

z^4=(3)^(1/2)+3i

Answer 1

This simplifies to: z4=3i+1.732051

Answer 2

\[z^4=\sqrt{3}+3i\]

Answer 3

I can't use a calculator

Answer 4

I got some pretty "out there" answers if anyone knowledgeable enough wants to take a look at them.

Answer 5

So then\[\large\rm z=\left(\sqrt3+3i\right)^{1/4}\]Hmm this angle isn't working out very nicely :[\[\large\rm \theta=\arctan\left(\frac{3}{\sqrt3}\right)\]\[\large\rm \theta=\arctan \sqrt3\]Oh nevermind, that's one of our special angles hehe.

Answer 6

\[\large\rm \theta=\frac{\pi}{3}\]And\[\large\rm r=\sqrt{\sqrt3~^2+3^2}\]\[\large\rm r=\sqrt{12}=2\sqrt3\]

Answer 7

And then you can do some stuffffffffff...
you went offline :p ok maybe later